Encoder which generates prediction image to be used to encode current block

ABSTRACT

An encoder includes circuitry and memory connected to the circuitry. The circuitry, in operation: derives, as a first parameter, a total sum of absolute values of sums of horizontal gradient values respectively for pairs of relative pixel positions; derives, as a second parameter, a total sum of absolute values of sums of vertical gradient values respectively for the pairs of relative pixel positions; derives, as a third parameter, a total sum of horizontal-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fourth parameter, a total sum of vertical-related pixel difference values respectively for the pairs of relative pixel positions; derives, as a fifth parameter, a total sum of vertical-related sums of horizontal gradient values respectively for the pairs of relative pixel positions; and generates a prediction image to be used to encode the current block using the first, second, third, fourth, and fifth parameters.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a U.S. continuation application of PCT InternationalPatent Application Number PCT/JP2020/023329 filed on Jun. 15, 2020,claiming the benefit of priority of U.S. Provisional Patent ApplicationNo. 62/864,728 filed on Jun. 21, 2019, the entire contents of which arehereby incorporated by reference.

BACKGROUND 1. Technical Field

The present disclosure relates to video coding, and relates to, forexample, systems, constituent elements, methods, etc. in encoding anddecoding of videos.

2. Description of the Related Art

The video coding technology has been developed from H.261 and MPEG-1 toH.264/AVC (Advanced Video Coding), MPEG-LA, H.265 (ISO/IEC 23008-2HEVC)/HEVC (High Efficiency Video Coding), and H.266/VVC (VersatileVideo Codec). With this development, it is always required to improveand optimize video coding technology in order to process digital videodata the amount of which has kept increasing in various kinds ofapplications.

It is to be noted that H.265/HEVC relates to one example of aconventional standard related to the above-described video codingtechnology.

SUMMARY

For example, an encoder according to an aspect of the present disclosureis an encoder including circuitry and memory connected to the circuitry.In operation, the circuitry: derives an absolute value of a sum ofhorizontal gradient values which indicates an absolute value of a sum ofa horizontal gradient value at a relative pixel position in a firstrange and a horizontal gradient value at a relative pixel position in asecond range, for each of a plurality of pairs of a relative pixelposition in the first range and a relative pixel position in the secondrange among a plurality of pairs of relative pixel positions, the firstrange including a first reference block for a current block, the secondrange including a second reference block for the current block, theplurality of pairs of relative pixel positions being determined commonlyand relatively for the first range and the second range; derives, as afirst parameter, a total sum of a plurality of absolute values of sumsof horizontal gradient values derived respectively for the plurality ofpairs of relative pixel positions; derives an absolute value of a sum ofvertical gradient values which indicates an absolute value of a sum of avertical gradient value at the relative pixel position in the firstrange and a vertical gradient value at the relative pixel position inthe second range, for each of the plurality of pairs of relative pixelpositions; derives, as a second parameter, a total sum of a plurality ofabsolute values of sums of vertical gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; derives, foreach of the plurality of pairs of relative pixel positions, a pixeldifference value which indicates a difference between the pixel value atthe relative pixel position in the first range and the pixel value atthe relative pixel position in the second range; inverts or maintains aplus or minus sign of the pixel difference value derived for each of theplurality of pairs of relative pixel positions, according to a plus orminus sign of the sum of the horizontal gradient values which indicatesthe sum of the horizontal gradient value at the relative pixel positionin the first range and the horizontal gradient value at the relativepixel position in the second range, and derives a horizontal-relatedpixel difference value which indicates a pixel difference value derivedfor the pair of relative pixel positions, the horizontal-related pixeldifference value having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the horizontalgradient values; derives, as a third parameter, a total sum of aplurality horizontal-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverts or maintains a plus or minus sign of the pixel difference valuederived for each of the plurality of pairs of relative pixel positions,according to a plus or minus sign of a sum of vertical gradient valueswhich indicates a sum of the vertical gradient value at the relativepixel position in the first range and the vertical gradient value at therelative pixel position in the second range, and derives avertical-related pixel difference value which indicates a pixeldifference value derived for the pair of relative pixel positions, thevertical-related pixel difference value having the plus or minus signinverted or maintained according to the plus or minus sign of the sum ofthe vertical gradient values; derives, as a fourth parameter, a totalsum of a plurality of vertical-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverts or maintains a plus or minus sign of the sum of the horizontalgradient values derived for each of the plurality of pairs of relativepixel positions, according to the plus or minus sign of the sum of thevertical gradient values, and derives a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; derives, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generates aprediction image to be used to encode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

Some of implementations of embodiments according to the presentdisclosure may: improve coding efficiency; simplify an encoding/decodingprocess; increase an encoding and/or decoding speed; and efficientlyselect appropriate components/operations to be used for encoding anddecoding, such as appropriate filters, block sizes, motion vectors,reference pictures, reference blocks, etc.

Further benefits and advantages according to one or more aspects of thepresent disclosure will become apparent from the Specification and theDrawings. These benefits and advantages are obtainable by featuresdescribed in some embodiments, the Specification, and the Drawings.However, all the features do not always need to be provided to obtainone or more of the advantages and/or effects.

It is to be noted that these general or specific aspects may beimplemented as a system, a method, an integrated circuit, a computerprogram, a recording medium, or any combination of these.

BRIEF DESCRIPTION OF DRAWINGS

These and other objects, advantages and features of the disclosure willbecome apparent from the following description thereof taken inconjunction with the accompanying drawings that illustrate a specificembodiment of the present disclosure.

FIG. 1 is a block diagram illustrating a functional configuration of anencoder according to an embodiment;

FIG. 2 is a flow chart indicating one example of an overall encodingprocess performed by the encoder;

FIG. 3 is a conceptual diagram illustrating one example of blocksplitting;

FIG. 4A is a conceptual diagram illustrating one example of a sliceconfiguration;

FIG. 4B is a conceptual diagram illustrating one example of a tileconfiguration;

FIG. 5A is a chart indicating transform basis functions for varioustransform types;

FIG. 5B is a conceptual diagram illustrating example spatially varyingtransforms (SVT);

FIG. 6A is a conceptual diagram illustrating one example of a filtershape used in an adaptive loop filter (ALF);

FIG. 6B is a conceptual diagram illustrating another example of a filtershape used in an ALF;

FIG. 6C is a conceptual diagram illustrating another example of a filtershape used in an ALF;

FIG. 7 is a block diagram indicating one example of a specificconfiguration of a loop filter which functions as a deblocking filter(DBF);

FIG. 8 is a conceptual diagram indicating an example of a deblockingfilter having a symmetrical filtering characteristic with respect to ablock boundary;

FIG. 9 is a conceptual diagram for illustrating a block boundary onwhich a deblocking filter process is performed;

FIG. 10 is a conceptual diagram indicating examples of Bs values;

FIG. 11 is a flow chart illustrating one example of a process performedby a prediction processor of the encoder;

FIG. 12 is a flow chart illustrating another example of a processperformed by the prediction processor of the encoder;

FIG. 13 is a flow chart illustrating another example of a processperformed by the prediction processor of the encoder;

FIG. 14 is a conceptual diagram illustrating sixty-seven intraprediction modes used in intra prediction in an embodiment;

FIG. 15 is a flow chart illustrating an example basic processing flow ofinter prediction;

FIG. 16 is a flow chart illustrating one example of derivation of motionvectors;

FIG. 17 is a flow chart illustrating another example of derivation ofmotion vectors;

FIG. 18 is a flow chart illustrating another example of derivation ofmotion vectors;

FIG. 19 is a flow chart illustrating an example of inter prediction innormal inter mode;

FIG. 20 is a flow chart illustrating an example of inter prediction inmerge mode;

FIG. 21 is a conceptual diagram for illustrating one example of a motionvector derivation process in merge mode;

FIG. 22 is a flow chart illustrating one example of frame rate upconversion (FRUC) process;

FIG. 23 is a conceptual diagram for illustrating one example of patternmatching (bilateral matching) between two blocks along a motiontrajectory;

FIG. 24 is a conceptual diagram for illustrating one example of patternmatching (template matching) between a template in a current picture anda block in a reference picture;

FIG. 25A is a conceptual diagram for illustrating one example ofderiving a motion vector of each sub-block based on motion vectors of aplurality of neighboring blocks;

FIG. 25B is a conceptual diagram for illustrating one example ofderiving a motion vector of each sub-block in affine mode in which threecontrol points are used;

FIG. 26A is a conceptual diagram for illustrating an affine merge mode;

FIG. 26B is a conceptual diagram for illustrating an affine merge modein which two control points are used;

FIG. 26C is a conceptual diagram for illustrating an affine merge modein which three control points are used:

FIG. 27 is a flow chart illustrating one example of a process in affinemerge mode;

FIG. 28A is a conceptual diagram for illustrating an affine inter modein which two control points are used;

FIG. 28B is a conceptual diagram for illustrating an affine inter modein which three control points are used;

FIG. 29 is a flow chart illustrating one example of a process in affineinter mode;

FIG. 30A is a conceptual diagram for illustrating an affine inter modein which a current block has three control points and a neighboringblock has two control points;

FIG. 30B is a conceptual diagram for illustrating an affine inter modein which a current block has two control points and a neighboring blockhas three control points;

FIG. 31A is a flow chart illustrating a merge mode process includingdecoder motion vector refinement (DMVR);

FIG. 31B is a conceptual diagram for illustrating one example of a DMVRprocess;

FIG. 32 is a flow chart illustrating one example of generation of aprediction image;

FIG. 33 is a flow chart illustrating another example of generation of aprediction image;

FIG. 34 is a flow chart illustrating another example of generation of aprediction image;

FIG. 35 is a flow chart illustrating one example of a prediction imagecorrection process performed by an overlapped block motion compensation(OBMC) process;

FIG. 36 is a conceptual diagram for illustrating one example of aprediction image correction process performed by an OBMC process;

FIG. 37 is a conceptual diagram for illustrating generation of twotriangular prediction images;

FIG. 38 is a conceptual diagram for illustrating a model assuminguniform linear motion;

FIG. 39 is a conceptual diagram for illustrating one example of aprediction image generation method using a luminance correction processperformed by a local illumination compensation (LIC) process;

FIG. 40 is a block diagram illustrating a mounting example of theencoder;

FIG. 41 is a block diagram illustrating a functional configuration of adecoder according to an embodiment;

FIG. 42 is a flow chart illustrating one example of an overall decodingprocess performed by the decoder;

FIG. 43 is a flow chart illustrating one example of a process performedby a prediction processor of the decoder;

FIG. 44 is a flow chart illustrating another example of a processperformed by the prediction processor of the decoder;

FIG. 45 is a flow chart illustrating an example of inter prediction innormal inter mode in the decoder;

FIG. 46 is a block diagram illustrating a mounting example of thedecoder;

FIG. 47 is a flow chart indicating one example of inter predictionaccording to BIO;

FIG. 48 is a diagram illustrating one example of a functionalconfiguration of an inter predictor which performs inter predictionaccording to BIO;

FIG. 49 is a flow chart indicating a first specific example of adecoding process based on BIO according to an embodiment;

FIG. 50 is a conceptual diagram illustrating an example of calculatinghorizontal gradient values according to the embodiment;

FIG. 51 is a conceptual diagram illustrating an example of calculatingvertical gradient values according to the embodiment;

FIG. 52 is a flow chart indicating a third specific example of adecoding process based on BIO according to an embodiment;

FIG. 53 is a flow chart indicating a fourth specific example of adecoding process based on BIO according to an embodiment;

FIG. 54 is a flow chart indicating an operation performed by an encoderaccording to the embodiment;

FIG. 55 is a flow chart indicating an operation performed by a decoderaccording to the embodiment;

FIG. 56 is a block diagram illustrating an overall configuration of acontent providing system for implementing a content distributionservice;

FIG. 57 is a conceptual diagram illustrating one example of an encodingstructure in scalable encoding;

FIG. 58 is a conceptual diagram illustrating one example of an encodingstructure in scalable encoding;

FIG. 59 is a conceptual diagram illustrating an example of a displayscreen of a web page;

FIG. 60 is a conceptual diagram illustrating an example of a displayscreen of a web page;

FIG. 61 is a block diagram illustrating one example of a smartphone; and

FIG. 62 is a block diagram illustrating an example of a configuration ofa smartphone.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In recent years, video encoding using a bi-directional optical flow hasbeen studied. The bi-directional optical flow is also referred to as BIOor BDOF.

For example, in the bi-directional optical flow, a prediction image isgenerated based on an optical flow equation. More specifically, in thebi-directional optical flow, a prediction image having a predicted valueadjusted for each pixel is generated using a parameter derived based ona pixel value of a reference image for each block and a gradient valueof a reference image for the block. The use of the bi-directionaloptical flow provides a high possibility that a highly accurateprediction image is generated.

For example, the encoder encodes a difference image between a predictionimage and an original image. The decoder then decodes the differenceimage and adds the difference image and the prediction image to generatea reconstructed image. The use of the highly accurate prediction imagemay reduce the amount of codes of the difference image. In other words,the use of the bi-directional optical flow provides a high possibilitythat the amount of codes of a resulting video is reduced.

On the other hand, the parameter for use in the bi-directional opticalflow is derived based on the pixel value and a gradient value at eachpixel position in a reference image. For this reason, computationperformed for each pixel in the derivation of a parameter to be used inthe bi-directional optical flow may increase the amount of computation,which may increase the circuitry scale.

In view of this, for example, an encoder according to an aspect of thepresent disclosure is an encoder including circuitry; and memoryconnected to the circuitry. In operation, the circuitry: derives anabsolute value of a sum of horizontal gradient values which indicates anabsolute value of a sum of a horizontal gradient value at a relativepixel position in a first range and a horizontal gradient value at arelative pixel position in a second range, for each of a plurality ofpairs of a relative pixel position in the first range and a relativepixel position in the second range among a plurality of pairs ofrelative pixel positions, the first range including a first referenceblock for a current block, the second range including a second referenceblock for the current block, the plurality of pairs of relative pixelpositions being determined commonly and relatively for the first rangeand the second range; derives, as a first parameter, a total sum of aplurality of absolute values of sums of horizontal gradient valuesderived respectively for the plurality of pairs of relative pixelpositions; derives an absolute value of a sum of vertical gradientvalues which indicates an absolute value of a sum of a vertical gradientvalue at the relative pixel position in the first range and a verticalgradient value at the relative pixel position in the second range, foreach of the plurality of pairs of relative pixel positions; derives, asa second parameter, a total sum of a plurality of absolute values ofsums of vertical gradient values derived respectively for the pluralityof pairs of relative pixel positions; derives, for each of the pluralityof pairs of relative pixel positions, a pixel difference value whichindicates a difference between the pixel value at the relative pixelposition in the first range and the pixel value at the relative pixelposition in the second range; inverts or maintains a plus or minus signof the pixel difference value derived for each of the plurality of pairsof relative pixel positions, according to a plus or minus sign of thesum of the horizontal gradient values which indicates the sum of thehorizontal gradient value at the relative pixel position in the firstrange and the horizontal gradient value at the relative pixel positionin the second range, and derives a horizontal-related pixel differencevalue which indicates a pixel difference value derived for the pair ofrelative pixel positions, the horizontal-related pixel difference valuehaving the plus or minus sign inverted or maintained according to theplus or minus sign of the sum of the horizontal gradient values;derives, as a third parameter, a total sum of a pluralityhorizontal-related pixel difference values derived respectively for theplurality of pairs of relative pixel positions; inverts or maintains aplus or minus sign of the pixel difference value derived for each of theplurality of pairs of relative pixel positions, according to a plus orminus sign of a sum of vertical gradient values which indicates a sum ofthe vertical gradient value at the relative pixel position in the firstrange and the vertical gradient value at the relative pixel position inthe second range, and derives a vertical-related pixel difference valuewhich indicates a pixel difference value derived for the pair ofrelative pixel positions, the vertical-related pixel difference valuehaving the plus or minus sign inverted or maintained according to theplus or minus sign of the sum of the vertical gradient values; derives,as a fourth parameter, a total sum of a plurality of vertical-relatedpixel difference values derived respectively for the plurality of pairsof relative pixel positions; inverts or maintains a plus or minus signof the sum of the horizontal gradient values derived for each of theplurality of pairs of relative pixel positions, according to the plus orminus sign of the sum of the vertical gradient values, and derives avertical-related sum of horizontal gradient values which indicates a sumof the horizontal gradient values having the plus or minus sign invertedor maintained according to the plus or minus sign of the sum of thevertical gradient values; derives, as a fifth parameter, a total sum ofa plurality vertical-related sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions; andgenerates a prediction image to be used to encode the current blockusing the first parameter, the second parameter, the third parameter,the fourth parameter, and the fifth parameter.

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive the plurality ofparameters for generating the prediction image with a low amount ofcomputation. Accordingly, the processing amount in encoding may bereduced. In addition, the prediction image may be generatedappropriately, based on the plurality of parameters including theparameter related to the horizontal gradient values, the parameterrelated to the vertical gradient values, and the parameter related toboth the horizontal gradient values and the vertical gradient values.

For example, the circuitry derives: the first parameter according toExpression (11.1) described later: the second parameter according toExpression (11.2) described later: the third parameter according toExpression (11.3) described later: the fourth parameter according toExpression (11.4) described later; and the fifth parameter according toExpression (11.5) described later. In the expressions: Ω denotes a setof the plurality of pairs of relative pixel positions; [i, j] denoteseach of the relative pixel positions included in the plurality of pairsof relative pixel positions; for each of the plurality of pairs ofrelative pixel positions, I_(x) ⁰ denotes a horizontal gradient value ata relative pixel position in the first range, and I_(x) ¹ denotes ahorizontal gradient value at a relative pixel position in the secondrange; for each of the plurality of pairs of relative pixel positions,I_(y) ⁰ denotes a vertical gradient value at a relative pixel positionin the first range, and I_(y) ¹ denotes a vertical gradient value at arelative pixel position in the second range; I⁰ denotes a pixel value atthe relative pixel position in the first range; I¹ denotes a pixel valueat the relative pixel position in the second range; abs (I_(x) ¹+I_(x)⁰) denotes an absolute value of I_(x) ¹+I_(x) ⁰; sign (I_(x) ¹+I_(x) ⁰)denotes a plus or minus sign of I_(x) ¹+I_(x) ⁰; abs (I_(y) ¹+I_(y) ⁰)denotes an absolute value of I_(y) ¹+I_(y) ⁰; and sign (I_(y) ¹+I_(y) ⁰)denotes a plus or minus sign of I_(y) ¹+I_(y) ⁰.

In this way, the plurality of parameters may be derived with a lowamount of computation using the pixel values, the horizontal gradientvalues, and the vertical gradient values.

In addition, for example, the circuitry: derives a sixth parameter bydividing the third parameter by the first parameter; derives a seventhparameter by subtracting a product of the fifth parameter and the sixthparameter from the fourth parameter, and dividing a result of thesubtraction by the second parameter; and generates the prediction imageusing the sixth parameter and the seventh parameter.

In this way, a plurality of parameters may be appropriately narroweddown to two parameters corresponding to the horizontal direction and thevertical direction. The parameter related to the horizontal gradientvalues may be appropriately incorporated in the parameter correspondingto the horizontal direction. The parameter related to the verticalgradient values, the parameter related to both the horizontal gradientvalues and the vertical gradient values, and the parameter correspondingto the horizontal direction may be appropriately incorporated in theparameter corresponding to the vertical direction. The prediction imagemay be appropriately generated using the two parameters.

In addition, for example, the circuitry derives: the sixth parameteraccording to Expression (10.8) described later; and the seventhparameter according to Expression (10.9) described later. In theexpressions: sG_(x) denotes the first parameter; sG_(y) denotes thesecond parameter; sG_(x)dI denotes the third parameter; sG_(y)dI denotesthe fourth parameter; sG_(x)G_(y) denotes the fifth parameter; u denotesthe sixth parameter; and Bits is a function which returns a valueobtainable by rounding up a binary logarithm of an argument to aninteger.

In this way, the two parameters corresponding to the horizontaldirection and the vertical direction may be derived with a low amount ofcomputation.

In addition, for example, the circuitry generates the prediction imageby deriving a prediction pixel value at a position of a current pixelincluded in the current block, using: a first pixel value at a firstpixel position corresponding to the position of the current pixel in thefirst reference block; a first horizontal gradient value at the firstpixel position; a first vertical gradient value at the first pixelposition; a second pixel value at a second pixel position correspondingto the position of the current pixel in the second reference block; asecond horizontal gradient value at the second pixel position; a secondvertical gradient value at the second pixel position; the sixthparameter; and the seventh parameter.

This provides a possibility that a prediction image is generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction, and the two parameterscorresponding to the horizontal direction and the vertical direction areappropriately reflected on the prediction image.

In addition, for example, the circuitry derives the prediction pixelvalue by dividing, by 2, a sum of the first pixel value, the secondpixel value, a first correction value, and a second correction value.The first correction value corresponds to a product of a differencebetween the first horizontal gradient value and the second horizontalgradient value and the sixth parameter, and the second correction valuecorresponds to a product of a difference between the first verticalgradient value and the second vertical gradient value and the seventhparameter.

In this way, the prediction image may be appropriately generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction.

In addition, for example, the circuitry derives: the prediction pixelvalue according to Expression (10.10). In the expression: I⁰ denotes thefirst pixel value; I¹ denotes the second pixel value; u denotes thesixth parameter; I_(x) ⁰ denotes the first horizontal gradient value;I_(x) ¹ denotes the second horizontal gradient value; v denotes theseventh parameter; I_(y) ⁰ denotes the first vertical gradient value;and I_(y) ¹ denotes the second vertical gradient value.

In this way, the prediction image may be appropriately generatedaccording to an expression related to, for example, the two parameterscorresponding to the horizontal direction and the vertical direction.

Furthermore, for example, a decoder according to an aspect of thepresent disclosure is a decoder including circuitry and memory connectedto the circuitry. In operation, the circuitry: derives an absolute valueof a sum of horizontal gradient values which indicates an absolute valueof a sum of a horizontal gradient value at a relative pixel position ina first range and a horizontal gradient value at a relative pixelposition in a second range, for each of a plurality of pairs of arelative pixel position in the first range and a relative pixel positionin the second range among a plurality of pairs of relative pixelpositions, the first range including a first reference block for acurrent block, the second range including a second reference block forthe current block, the plurality of pairs of relative pixel positionsbeing determined commonly and relatively for the first range and thesecond range; derives, as a first parameter, a total sum of a pluralityof absolute values of sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions;derives an absolute value of a sum of vertical gradient values whichindicates an absolute value of a sum of a vertical gradient value at therelative pixel position in the first range and a vertical gradient valueat the relative pixel position in the second range, for each of theplurality of pairs of relative pixel positions; derives, as a secondparameter, a total sum of a plurality of absolute values of sums ofvertical gradient values derived respectively for the plurality of pairsof relative pixel positions; derives, for each of the plurality of pairsof relative pixel positions, a pixel difference value which indicates adifference between the pixel value at the relative pixel position in thefirst range and the pixel value at the relative pixel position in thesecond range; inverts or maintains a plus or minus sign of the pixeldifference value derived for each of the plurality of pairs of relativepixel positions, according to a plus or minus sign of the sum of thehorizontal gradient values which indicates the sum of the horizontalgradient value at the relative pixel position in the first range and thehorizontal gradient value at the relative pixel position in the secondrange, and derives a horizontal-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the horizontal-related pixel difference value havingthe plus or minus sign inverted or maintained according to the plus orminus sign of the sum of the horizontal gradient values; derives, as athird parameter, a total sum of a plurality horizontal-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverts or maintains a plus or minus sign ofthe pixel difference value derived for each of the plurality of pairs ofrelative pixel positions, according to a plus or minus sign of a sum ofvertical gradient values which indicates a sum of the vertical gradientvalue at the relative pixel position in the first range and the verticalgradient value at the relative pixel position in the second range, andderives a vertical-related pixel difference value which indicates apixel difference value derived for the pair of relative pixel positions,the vertical-related pixel difference value having the plus or minussign inverted or maintained according to the plus or minus sign of thesum of the vertical gradient values; derives, as a fourth parameter, atotal sum of a plurality of vertical-related pixel difference valuesderived respectively for the plurality of pairs of relative pixelpositions; inverts or maintains a plus or minus sign of the sum of thehorizontal gradient values derived for each of the plurality of pairs ofrelative pixel positions, according to the plus or minus sign of the sumof the vertical gradient values, and derives a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; derives, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generates aprediction image to be used to decode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive the plurality ofparameters for generating the prediction image with a low amount ofcomputation. Accordingly, the processing amount in decoding may bereduced. In addition, the prediction image may be generatedappropriately, based on the plurality of parameters including theparameter related to the horizontal gradient values, the parameterrelated to the vertical gradient values, and the parameter related toboth the horizontal gradient values and the vertical gradient values.

In addition, for example, the circuitry derives: the first parameteraccording to Expression (11.1) described later: the second parameteraccording to Expression (11.2) described later: the third parameteraccording to Expression (11.3) described later: the fourth parameteraccording to Expression (11.4) described later; and the fifth parameteraccording to Expression (11.5) described later. In the expressions: Ωdenotes a set of the plurality of pairs of relative pixel positions; [i,j] denotes each of the relative pixel positions included in theplurality of pairs of relative pixel positions; for each of theplurality of pairs of relative pixel positions, I_(x) ⁰ denotes ahorizontal gradient value at a relative pixel position in the firstrange, and I_(x) ¹ denotes a horizontal gradient value at a relativepixel position in the second range; for each of the plurality of pairsof relative pixel positions, I_(y) ⁰ denotes a vertical gradient valueat a relative pixel position in the first range, and I_(y) ¹ denotes avertical gradient value at a relative pixel position in the secondrange; I⁰ denotes a pixel value at the relative pixel position in thefirst range; I¹ denotes a pixel value at the relative pixel position inthe second range; abs (I_(x) ¹+I_(x) ⁰) denotes an absolute value ofI_(x) ¹+I_(x) ⁰; sign (I_(x) ¹+I_(x) ⁰) denotes a plus or minus sign ofI_(x) ¹+I_(x) ⁰; abs (I_(y) ¹+I_(y) ⁰) denotes an absolute value ofI_(y) ¹+I_(y) ⁰; and sign (I_(y) ¹+I_(y) ⁰) denotes a plus or minus signof I_(y) ¹+I_(y) ⁰.

In this way, the plurality of parameters may be derived with a lowamount of computation using the pixel values, the horizontal gradientvalues, and the vertical gradient values.

In addition, for example, the circuitry: derives a sixth parameter bydividing the third parameter by the first parameter; derives a seventhparameter by subtracting a product of the fifth parameter and the sixthparameter from the fourth parameter, and dividing a result of thesubtraction by the second parameter; and generates the prediction imageusing the sixth parameter and the seventh parameter.

In this way, a plurality of parameters may be appropriately integratedto two parameters corresponding to a horizontal direction and a verticaldirection. The parameter related to the horizontal gradient values maybe appropriately incorporated in the parameter corresponding to thehorizontal direction. The parameter related to the vertical gradientvalues, the parameter related to both the horizontal gradient values andthe vertical gradient values, and the parameter corresponding to thehorizontal direction may be appropriately incorporated in the parametercorresponding to the vertical direction. The prediction image may beappropriately generated using the two parameters.

In addition, for example, the circuitry derives: the sixth parameteraccording to Expression (10.8) described later; and the seventhparameter according to Expression (10.9) described later. In theexpressions: sG_(x) denotes the first parameter; sG_(y) denotes thesecond parameter; sG_(x)dI denotes the third parameter; sG_(y)dI denotesthe fourth parameter; sG_(x)G_(y) denotes the fifth parameter; u denotesthe sixth parameter; and Bits is a function which returns a valueobtainable by rounding up a binary logarithm of an argument to aninteger.

In this way, the two parameters corresponding to the horizontaldirection and the vertical direction may be derived with a low amount ofcomputation.

In addition, for example, the circuitry generates the prediction imageby deriving a prediction pixel value at a position of a current pixelincluded in the current block, using: a first pixel value at a firstpixel position corresponding to the position of the current pixel in thefirst reference block; a first horizontal gradient value at the firstpixel position; a first vertical gradient value at the first pixelposition; a second pixel value at a second pixel position correspondingto the position of the current pixel in the second reference block; asecond horizontal gradient value at the second pixel position; a secondvertical gradient value at the second pixel position; the sixthparameter; and the seventh parameter.

This provides a possibility that a prediction image is generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction, and the two parameterscorresponding to the horizontal direction and the vertical direction areappropriately reflected on the prediction image.

In addition, for example, the circuitry derives the prediction pixelvalue by dividing, by 2, a sum of the first pixel value, the secondpixel value, a first correction value, and a second correction value.The first correction value corresponds to a product of a differencebetween the first horizontal gradient value and the second horizontalgradient value and the sixth parameter, and the second correction valuecorresponds to a product of a difference between the first verticalgradient value and the second vertical gradient value and the seventhparameter.

In this way, the prediction image may be appropriately generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction.

In addition, for example, the circuitry derives: the prediction pixelvalue according to Expression (10.10). In the expression: I⁰ denotes thefirst pixel value; I¹ denotes the second pixel value; u denotes thesixth parameter; I_(x) ⁰ denotes the first horizontal gradient value;I_(x) ¹ denotes the second horizontal gradient value; v denotes theseventh parameter; I_(y) ⁰ denotes the first vertical gradient value;and I_(y) ¹ denotes the second vertical gradient value.

In this way, the prediction image may be appropriately generatedaccording to an expression related to, for example, the two parameterscorresponding to the horizontal direction and the vertical direction.

Furthermore, for example, an encoding method according to an aspect ofthe present disclosure is an encoding method including: deriving anabsolute value of a sum of horizontal gradient values which indicates anabsolute value of a sum of a horizontal gradient value at a relativepixel position in a first range and a horizontal gradient value at arelative pixel position in a second range, for each of a plurality ofpairs of a relative pixel position in the first range and a relativepixel position in the second range among a plurality of pairs ofrelative pixel positions, the first range including a first referenceblock for a current block, the second range including a second referenceblock for the current block, the plurality of pairs of relative pixelpositions being determined commonly and relatively for the first rangeand the second range; deriving, as a first parameter, a total sum of aplurality of absolute values of sums of horizontal gradient valuesderived respectively for the plurality of pairs of relative pixelpositions; deriving an absolute value of a sum of vertical gradientvalues which indicates an absolute value of a sum of a vertical gradientvalue at the relative pixel position in the first range and a verticalgradient value at the relative pixel position in the second range, foreach of the plurality of pairs of relative pixel positions; deriving, asa second parameter, a total sum of a plurality of absolute values ofsums of vertical gradient values derived respectively for the pluralityof pairs of relative pixel positions; deriving, for each of theplurality of pairs of relative pixel positions, a pixel difference valuewhich indicates a difference between the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range; inverting or maintaining a plus orminus sign of the pixel difference value derived for each of theplurality of pairs of relative pixel positions, according to a plus orminus sign of the sum of the horizontal gradient values which indicatesthe sum of the horizontal gradient value at the relative pixel positionin the first range and the horizontal gradient value at the relativepixel position in the second range, and deriving a horizontal-relatedpixel difference value which indicates a pixel difference value derivedfor the pair of relative pixel positions, the horizontal-related pixeldifference value having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the horizontalgradient values; deriving, as a third parameter, a total sum of aplurality horizontal-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverting or maintaining a plus or minus sign of the pixel differencevalue derived for each of the plurality of pairs of relative pixelpositions, according to a plus or minus sign of a sum of verticalgradient values which indicates a sum of the vertical gradient value atthe relative pixel position in the first range and the vertical gradientvalue at the relative pixel position in the second range, and deriving avertical-related pixel difference value which indicates a pixeldifference value derived for the pair of relative pixel positions, thevertical-related pixel difference value having the plus or minus signinverted or maintained according to the plus or minus sign of the sum ofthe vertical gradient values; deriving, as a fourth parameter, a totalsum of a plurality of vertical-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverting or maintaining a plus or minus sign of the sum of thehorizontal gradient values derived for each of the plurality of pairs ofrelative pixel positions, according to the plus or minus sign of the sumof the vertical gradient values, and deriving a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; deriving, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generating aprediction image to be used to encode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive the plurality ofparameters for generating the prediction image with a low amount ofcomputation. Accordingly, the processing amount in encoding may bereduced. In addition, the prediction image may be generatedappropriately, based on the plurality of parameters including theparameter related to the horizontal gradient values, the parameterrelated to the vertical gradient values, and the parameter related toboth the horizontal gradient values and the vertical gradient values.

Furthermore, for example, a decoding method according to an aspect ofthe present disclosure is a decoding method including: deriving anabsolute value of a sum of horizontal gradient values which indicates anabsolute value of a sum of a horizontal gradient value at a relativepixel position in a first range and a horizontal gradient value at arelative pixel position in a second range, for each of a plurality ofpairs of a relative pixel position in the first range and a relativepixel position in the second range among a plurality of pairs ofrelative pixel positions, the first range including a first referenceblock for a current block, the second range including a second referenceblock for the current block, the plurality of pairs of relative pixelpositions being determined commonly and relatively for the first rangeand the second range; deriving, as a first parameter, a total sum of aplurality of absolute values of sums of horizontal gradient valuesderived respectively for the plurality of pairs of relative pixelpositions; deriving an absolute value of a sum of vertical gradientvalues which indicates an absolute value of a sum of a vertical gradientvalue at the relative pixel position in the first range and a verticalgradient value at the relative pixel position in the second range, foreach of the plurality of pairs of relative pixel positions; deriving, asa second parameter, a total sum of a plurality of absolute values ofsums of vertical gradient values derived respectively for the pluralityof pairs of relative pixel positions; deriving, for each of theplurality of pairs of relative pixel positions, a pixel difference valuewhich indicates a difference between the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range; inverting or maintaining a plus orminus sign of the pixel difference value derived for each of theplurality of pairs of relative pixel positions, according to a plus orminus sign of the sum of the horizontal gradient values which indicatesthe sum of the horizontal gradient value at the relative pixel positionin the first range and the horizontal gradient value at the relativepixel position in the second range, and deriving a horizontal-relatedpixel difference value which indicates a pixel difference value derivedfor the pair of relative pixel positions, the horizontal-related pixeldifference value having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the horizontalgradient values; deriving, as a third parameter, a total sum of aplurality horizontal-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverting or maintaining a plus or minus sign of the pixel differencevalue derived for each of the plurality of pairs of relative pixelpositions, according to a plus or minus sign of a sum of verticalgradient values which indicates a sum of the vertical gradient value atthe relative pixel position in the first range and the vertical gradientvalue at the relative pixel position in the second range, and deriving avertical-related pixel difference value which indicates a pixeldifference value derived for the pair of relative pixel positions, thevertical-related pixel difference value having the plus or minus signinverted or maintained according to the plus or minus sign of the sum ofthe vertical gradient values; deriving, as a fourth parameter, a totalsum of a plurality of vertical-related pixel difference values derivedrespectively for the plurality of pairs of relative pixel positions;inverting or maintaining a plus or minus sign of the sum of thehorizontal gradient values derived for each of the plurality of pairs ofrelative pixel positions, according to the plus or minus sign of the sumof the vertical gradient values, and deriving a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; deriving, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generating aprediction image to be used to decode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive a plurality of parametersfor generating a prediction image with a low amount of computation.Accordingly, the processing amount in decoding may be reduced. Inaddition, the prediction image may be generated appropriately, based onthe plurality of parameters including the parameter related to thehorizontal gradient values, the parameter related to the verticalgradient values, and the parameter related to both the horizontalgradient values and the vertical gradient values.

Alternatively, an encoder according to an aspect of the presentdisclosure is an encoder which includes a splitter, an intra predictor,an inter predictor, a transformer, a quantizer, and an entropy encoder.

The splitter splits a current picture to be encoded included in thevideo into a plurality of blocks. The intra predictor performs intraprediction for generating a prediction image for a current block to beencoded in the current picture, using a reference image in the currentpicture. The inter predictor performs inter prediction for generating aprediction image for a current block to be encoded, using a referenceimage in a reference picture different from the current picture.

The transformer transforms a prediction error signal between (i) eitherthe prediction image generated by the intra predictor or the predictionimage generated by the inter predictor and (ii) the image of the currentblock, to generate a transform coefficient signal of the current block.The quantizer quantizes the transform coefficient signal. The entropyencoder encodes the quantized transform coefficient signal.

Furthermore, for example, the inter predictor: derives an absolute valueof a sum of horizontal gradient values which indicates an absolute valueof a sum of a horizontal gradient value at a relative pixel position ina first range and a horizontal gradient value at a relative pixelposition in a second range, for each of a plurality of pairs of arelative pixel position in the first range and a relative pixel positionin the second range among a plurality of pairs of relative pixelpositions, the first range including a first reference block for acurrent block, the second range including a second reference block forthe current block, the plurality of pairs of relative pixel positionsbeing determined commonly and relatively for the first range and thesecond range; derives, as a first parameter, a total sum of a pluralityof absolute values of sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions;derives an absolute value of a sum of vertical gradient values whichindicates an absolute value of a sum of a vertical gradient value at therelative pixel position in the first range and a vertical gradient valueat the relative pixel position in the second range, for each of theplurality of pairs of relative pixel positions; derives, as a secondparameter, a total sum of a plurality of absolute values of sums ofvertical gradient values derived respectively for the plurality of pairsof relative pixel positions; derives, for each of the plurality of pairsof relative pixel positions, a pixel difference value which indicates adifference between the pixel value at the relative pixel position in thefirst range and the pixel value at the relative pixel position in thesecond range; inverts or maintains a plus or minus sign of the pixeldifference value derived for each of the plurality of pairs of relativepixel positions, according to a plus or minus sign of the sum of thehorizontal gradient values which indicates the sum of the horizontalgradient value at the relative pixel position in the first range and thehorizontal gradient value at the relative pixel position in the secondrange, and derives a horizontal-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the horizontal-related pixel difference value havingthe plus or minus sign inverted or maintained according to the plus orminus sign of the sum of the horizontal gradient values; derives, as athird parameter, a total sum of a plurality horizontal-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverts or maintains a plus or minus sign ofthe pixel difference value derived for each of the plurality of pairs ofrelative pixel positions, according to a plus or minus sign of a sum ofvertical gradient values which indicates a sum of the vertical gradientvalue at the relative pixel position in the first range and the verticalgradient value at the relative pixel position in the second range, andderives a vertical-related pixel difference value which indicates apixel difference value derived for the pair of relative pixel positions,the vertical-related pixel difference value having the plus or minussign inverted or maintained according to the plus or minus sign of thesum of the vertical gradient values; derives, as a fourth parameter, atotal sum of a plurality of vertical-related pixel difference valuesderived respectively for the plurality of pairs of relative pixelpositions; inverts or maintains a plus or minus sign of the sum of thehorizontal gradient values derived for each of the plurality of pairs ofrelative pixel positions, according to the plus or minus sign of the sumof the vertical gradient values, and derives a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; derives, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generates aprediction image to be used to encode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

Alternatively, for example, a decoder according to an aspect of thepresent disclosure includes an entropy decoder, an inverse quantizer, aninverse transformer, an intra predictor, an inter predictor, and anadder (reconstructor).

The entropy decoder decodes a quantized transform coefficient signal ofa current block to be decoded in a current picture to be decoded in thevideo. The inverse quantizer inverse quantizes the quantized transformcoefficient signal. The inverse transformer inverse transforms thetransform coefficient signal to obtain a prediction error signal of thecurrent block.

The intra predictor performs intra prediction for generating theprediction image for a current block to be decoded, using a referenceimage in a current picture to be decoded. The inter predictor performsinter prediction for generating a prediction image for a current blockto be decoded, using a reference image in a reference picture differentfrom the current picture. The adder adds the prediction error signal andeither the prediction image generated by the intra predictor or theprediction image generated by the inter predictor to reconstruct animage of the current block.

Furthermore, for example, the inter predictor: derives an absolute valueof a sum of horizontal gradient values which indicates an absolute valueof a sum of a horizontal gradient value at a relative pixel position ina first range and a horizontal gradient value at a relative pixelposition in a second range, for each of a plurality of pairs of arelative pixel position in the first range and a relative pixel positionin the second range among a plurality of pairs of relative pixelpositions, the first range including a first reference block for acurrent block, the second range including a second reference block forthe current block, the plurality of pairs of relative pixel positionsbeing determined commonly and relatively for the first range and thesecond range; derives, as a first parameter, a total sum of a pluralityof absolute values of sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions;derives an absolute value of a sum of vertical gradient values whichindicates an absolute value of a sum of a vertical gradient value at therelative pixel position in the first range and a vertical gradient valueat the relative pixel position in the second range, for each of theplurality of pairs of relative pixel positions; derives, as a secondparameter, a total sum of a plurality of absolute values of sums ofvertical gradient values derived respectively for the plurality of pairsof relative pixel positions; derives, for each of the plurality of pairsof relative pixel positions, a pixel difference value which indicates adifference between the pixel value at the relative pixel position in thefirst range and the pixel value at the relative pixel position in thesecond range; inverts or maintains a plus or minus sign of the pixeldifference value derived for each of the plurality of pairs of relativepixel positions, according to a plus or minus sign of the sum of thehorizontal gradient values which indicates the sum of the horizontalgradient value at the relative pixel position in the first range and thehorizontal gradient value at the relative pixel position in the secondrange, and derives a horizontal-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the horizontal-related pixel difference value havingthe plus or minus sign inverted or maintained according to the plus orminus sign of the sum of the horizontal gradient values; derives, as athird parameter, a total sum of a plurality horizontal-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverts or maintains a plus or minus sign ofthe pixel difference value derived for each of the plurality of pairs ofrelative pixel positions, according to a plus or minus sign of a sum ofvertical gradient values which indicates a sum of the vertical gradientvalue at the relative pixel position in the first range and the verticalgradient value at the relative pixel position in the second range, andderives a vertical-related pixel difference value which indicates apixel difference value derived for the pair of relative pixel positions,the vertical-related pixel difference value having the plus or minussign inverted or maintained according to the plus or minus sign of thesum of the vertical gradient values; derives, as a fourth parameter, atotal sum of a plurality of vertical-related pixel difference valuesderived respectively for the plurality of pairs of relative pixelpositions; inverts or maintains a plus or minus sign of the sum of thehorizontal gradient values derived for each of the plurality of pairs ofrelative pixel positions, according to the plus or minus sign of the sumof the vertical gradient values, and derives a vertical-related sum ofhorizontal gradient values which indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues; derives, as a fifth parameter, a total sum of a pluralityvertical-related sums of horizontal gradient values derived respectivelyfor the plurality of pairs of relative pixel positions; and generates aprediction image to be used to decode the current block using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter.

Furthermore, these general or specific aspects may be implemented usinga system, an apparatus, a method, an integrated circuit, a computerprogram, or a non-transitory computer-readable recording medium such asa CD-ROM, or any combination of systems, apparatuses, methods,integrated circuits, computer programs, or computer-readable recordingmedia.

Hereinafter, embodiments will be described with reference to thedrawings. Note that the embodiments described below each show a generalor specific example. The numerical values, shapes, materials,components, the arrangement and connection of the components, steps, therelation and order of the steps, etc., indicated in the followingembodiments are mere examples, and are not intended to limit the scopeof the claims.

Embodiments of an encoder and a decoder will be described below. Theembodiments are examples of an encoder and a decoder to which theprocesses and/or configurations presented in the description of aspectsof the present disclosure are applicable. The processes and/orconfigurations can also be implemented in an encoder and a decoderdifferent from those according to the embodiments. For example,regarding the processes and/or configurations as applied to theembodiments, any of the following may be implemented:

(1) Any of the components of the encoder or the decoder according to theembodiments presented in the description of aspects of the presentdisclosure may be substituted or combined with another componentpresented anywhere in the description of aspects of the presentdisclosure.

(2) In the encoder or the decoder according to the embodiments,discretionary changes may be made to functions or processes performed byone or more components of the encoder or the decoder, such as addition,substitution, removal, etc., of the functions or processes. For example,any function or process may be substituted or combined with anotherfunction or process presented anywhere in the description of aspects ofthe present disclosure.

(3) In methods implemented by the encoder or the decoder according tothe embodiments, discretionary changes may be made such as addition,substitution, and removal of one or more of the processes included inthe method. For example, any process in the method may be substituted orcombined with another process presented anywhere in the description ofaspects of the present disclosure.

(4) One or more components included in the encoder or the decoderaccording to embodiments may be combined with a component presentedanywhere in the description of aspects of the present disclosure, may becombined with a component including one or more functions presentedanywhere in the description of aspects of the present disclosure, andmay be combined with a component that implements one or more processesimplemented by a component presented in the description of aspects ofthe present disclosure.

(5) A component including one or more functions of the encoder or thedecoder according to the embodiments, or a component that implements oneor more processes of the encoder or the decoder according to theembodiments, may be combined or substituted with a component presentedanywhere in the description of aspects of the present disclosure, with acomponent including one or more functions presented anywhere in thedescription of aspects of the present disclosure, or with a componentthat implements one or more processes presented anywhere in thedescription of aspects of the present disclosure.

(6) In methods implemented by the encoder or the decoder according tothe embodiments, any of the processes included in the method may besubstituted or combined with a process presented anywhere in thedescription of aspects of the present disclosure or with anycorresponding or equivalent process.

(7) One or more processes included in methods implemented by the encoderor the decoder according to the embodiments may be combined with aprocess presented anywhere in the description of aspects of the presentdisclosure.

(8) The implementation of the processes and/or configurations presentedin the description of aspects of the present disclosure is not limitedto the encoder or the decoder according to the embodiments. For example,the processes and/or configurations may be implemented in a device usedfor a purpose different from the moving picture encoder or the movingpicture decoder disclosed in the embodiments.

[Encoder]

First, an encoder according to an embodiment will be described. FIG. 1is a block diagram illustrating a functional configuration of encoder100 according to the embodiment. Encoder 100 is a video encoder whichencodes a video in units of a block.

As illustrated in FIG. 1, encoder 100 is an apparatus which encodes animage in units of a block, and includes splitter 102, subtractor 104,transformer 106, quantizer 108, entropy encoder 110, inverse quantizer112, inverse transformer 114, adder 116, block memory 118, loop filter120, frame memory 122, intra predictor 124, inter predictor 126, andprediction controller 128.

Encoder 100 is implemented as, for example, a generic processor andmemory. In this case, when a software program stored in the memory isexecuted by the processor, the processor functions as splitter 102,subtractor 104, transformer 106, quantizer 108, entropy encoder 110,inverse quantizer 112, inverse transformer 114, adder 116, loop filter120, intra predictor 124, inter predictor 126, and prediction controller128. Alternatively, encoder 100 may be implemented as one or morededicated electronic circuits corresponding to splitter 102, subtractor104, transformer 106, quantizer 108, entropy encoder 110, inversequantizer 112, inverse transformer 114, adder 116, loop filter 120,intra predictor 124, inter predictor 126, and prediction controller 128.

Hereinafter, an overall flow of processes performed by encoder 100 isdescribed, and then each of constituent elements included in encoder 100will be described.

[Overall Flow of Encoding Process]

FIG. 2 is a flow chart indicating one example of an overall encodingprocess performed by encoder 100.

First, splitter 102 of encoder 100 splits each of pictures included inan input image which is a video into a plurality of blocks having afixed size (e.g., 128×128 pixels) (Step Sa_1). Splitter 102 then selectsa splitting pattern for the fixed-size block (also referred to as ablock shape) (Step Sa_2). In other words, splitter 102 further splitsthe fixed-size block into a plurality of blocks which form the selectedsplitting pattern. Encoder 100 performs, for each of the plurality ofblocks, Steps Sa_3 to Sa_9 for the block (that is a current block to beencoded).

In other words, a prediction processor which includes all or part ofintra predictor 124, inter predictor 126, and prediction controller 128generates a prediction signal (also referred to as a prediction block)of the current block to be encoded (also referred to as a current block)(Step Sa_3).

Next, subtractor 104 generates a difference between the current blockand a prediction block as a prediction residual (also referred to as adifference block) (Step Sa_4).

Next, transformer 106 transforms the difference block and quantizer 108quantizes the result, to generate a plurality of quantized coefficients(Step Sa_5). It is to be noted that the block having the plurality ofquantized coefficients is also referred to as a coefficient block.

Next, entropy encoder 110 encodes (specifically, entropy encodes) thecoefficient block and a prediction parameter related to generation of aprediction signal to generate an encoded signal (Step Sa_6). It is to benoted that the encoded signal is also referred to as an encodedbitstream, a compressed bitstream, or a stream.

Next, inverse quantizer 112 performs inverse quantization of thecoefficient block and inverse transformer 114 performs inverse transformof the result, to restore a plurality of prediction residuals (that is,a difference block) (Step Sa_7).

Next, adder 116 adds the prediction block to the restored differenceblock to reconstruct the current block as a reconstructed image (alsoreferred to as a reconstructed block or a decoded image block) (StepSa_8). In this way, the reconstructed image is generated.

When the reconstructed image is generated, loop filter 120 performsfiltering of the reconstructed image as necessary (Step Sa_9).

Encoder 100 then determines whether encoding of the entire picture hasbeen finished (Step Sa_10). When determining that the encoding has notyet been finished (No in Step Sa_10), processes from Step Sa_2 areexecuted repeatedly.

Although encoder 100 selects one splitting pattern for a fixed-sizeblock, and encodes each block according to the splitting pattern in theabove-described example, it is to be noted that each block may beencoded according to a corresponding one of a plurality of splittingpatterns. In this case, encoder 100 may evaluate a cost for each of theplurality of splitting patterns, and, for example, may select theencoded signal obtainable by encoding according to the splitting patternwhich yields the smallest cost as an encoded signal which is output.

As illustrated, the processes in Steps Sa_1 to Sa_10 are performedsequentially by encoder 100. Alternatively, two or more of the processesmay be performed in parallel, the processes may be reordered, etc.

[Splitter]

Splitter 102 splits each of pictures included in an input video into aplurality of blocks, and outputs each block to subtractor 104. Forexample, splitter 102 first splits a picture into blocks of a fixed size(for example, 128×128). Other fixed block sizes may be employed. Thefixed-size block is also referred to as a coding tree unit (CTU).Splitter 102 then splits each fixed-size block into blocks of variablesizes (for example, 64×64 or smaller), based on recursive quadtreeand/or binary tree block splitting. In other words, splitter 102 selectsa splitting pattern. The variable-size block is also referred to as acoding unit (CU), a prediction unit (PU), or a transform unit (TU). Itis to be noted that, in various kinds of processing examples, there isno need to differentiate between CU, PU, and TU; all or some of theblocks in a picture may be processed in units of a CU, a PU, or a TU.

FIG. 3 is a conceptual diagram illustrating one example of blocksplitting according to an embodiment. In FIG. 3, the solid linesrepresent block boundaries of blocks split by quadtree block splitting,and the dashed lines represent block boundaries of blocks split bybinary tree block splitting.

Here, block 10 is a square block having 128×128 pixels (128×128 block).This 128×128 block 10 is first split into four square 64×64 blocks(quadtree block splitting).

The upper-left 64×64 block is further vertically split into tworectangular 32×64 blocks, and the left 32×64 block is further verticallysplit into two rectangular 16×64 blocks (binary tree block splitting).As a result, the upper-left 64×64 block is split into two 16×64 blocks11 and 12 and one 32×64 block 13.

The upper-right 64×64 block is horizontally split into two rectangular64×32 blocks 14 and 15 (binary tree block splitting).

The lower-left 64×64 block is first split into four square 32×32 blocks(quadtree block splitting). The upper-left block and the lower-rightblock among the four 32×32 blocks are further split. The upper-left32×32 block is vertically split into two rectangle 16×32 blocks, and theright 16×32 block is further horizontally split into two 16×16 blocks(binary tree block splitting). The lower-right 32×32 block ishorizontally split into two 32×16 blocks (binary tree block splitting).As a result, the lower-left 64×64 block is split into 16×32 block 16,two 16×16 blocks 17 and 18, two 32×32 blocks 19 and 20, and two 32×16blocks 21 and 22.

The lower-right 64×64 block 23 is not split.

As described above, in FIG. 3, block 10 is split into thirteenvariable-size blocks 11 through 23 based on recursive quadtree andbinary tree block splitting. This type of splitting is also referred toas quadtree plus binary tree (QTBT) splitting.

It is to be noted that, in FIG. 3, one block is split into four or twoblocks (quadtree or binary tree block splitting), but splitting is notlimited to these examples. For example, one block may be split intothree blocks (ternary block splitting). Splitting including such ternaryblock splitting is also referred to as multi-type tree (MBT) splitting.

[Picture Structure: Slice/Tile]

A picture may be configured in units of one or more slices or tiles inorder to decode the picture in parallel. The picture configured in unitsof one or more slices or tiles may be configured by splitter 102.

Slices are basic encoding units included in a picture. A picture mayinclude, for example, one or more slices. In addition, a slice includesone or more successive coding tree units (CTU).

FIG. 4A is a conceptual diagram illustrating one example of a sliceconfiguration. For example, a picture includes 11×8 CTUs and is splitinto four slices (slices 1 to 4). Slice 1 includes sixteen CTUs, slice 2includes twenty-one CTUs, slice 3 includes twenty-nine CTUs. and slice 4includes twenty-two CTUs. Here, each CTU in the picture belongs to oneof the slices.

The shape of each slice is a shape obtainable by splitting the picturehorizontally. A boundary of each slice does not need to be coincide withan image end, and may be coincide with any of the boundaries betweenCTUs in the image. The processing order of the CTUs in a slice (anencoding order or a decoding order) is, for example, a raster-scanorder. A slice includes header information and encoded data. Features ofthe slice may be described in header information. The features include aCTU address of a top CTU in the slice, a slice type, etc.

A tile is a unit of a rectangular region included in a picture. Each oftiles may be assigned with a number referred to as TileId in raster-scanorder.

FIG. 4B is a conceptual diagram indicating an example of a tileconfiguration. For example, a picture includes 11×8 CTUs and is splitinto four tiles of rectangular regions (tiles 1 to 4). When tiles areused, the processing order of CTUs are changed from the processing orderin the case where no tile is used. When no tile is used, CTUs in apicture are processed in raster-scan order. When tiles are used, atleast one CTU in each of the tiles is processed in raster-scan order.For example, as illustrated in FIG. 4B, the processing order of the CTUsincluded in tile 1 is the order which starts from the left-end of thefirst row of tile 1 toward the right-end of the first row of tile 1 andthen starts from the left-end of the second row of tile 1 toward theright-end of the second row of tile 1.

It is to be noted that the one tile may include one or more slices, andone slice may include one or more tiles.

[Subtractor]

Subtractor 104 subtracts a prediction signal (prediction sample that isinput from prediction controller 128 indicated below) from an originalsignal (original sample) in units of a block input from splitter 102 andsplit by splitter 102. In other words, subtractor 104 calculatesprediction errors (also referred to as residuals) of a block to beencoded (hereinafter also referred to as a current block). Subtractor104 then outputs the calculated prediction errors (residuals) totransformer 106.

The original signal is a signal which has been input into encoder 100and represents an image of each picture included in a video (forexample, a luma signal and two chroma signals). Hereinafter, a signalrepresenting an image is also referred to as a sample.

[Transformer]

Transformer 106 transforms prediction errors in spatial domain intotransform coefficients in frequency domain, and outputs the transformcoefficients to quantizer 108. More specifically, transformer 106applies, for example, a defined discrete cosine transform (DCT) ordiscrete sine transform (DST) to prediction errors in spatial domain.The defined DCT or DST may be predefined.

It is to be noted that transformer 106 may adaptively select a transformtype from among a plurality of transform types, and transform predictionerrors into transform coefficients by using a transform basis functioncorresponding to the selected transform type. This sort of transform isalso referred to as explicit multiple core transform (EMT) or adaptivemultiple transform (AMT).

The transform types include, for example, DCT-II, DCT-V, DCT-VIII,DST-I, and DST-VII. FIG. 5A is a chart indicating transform basisfunctions for the example transform types. In FIG. 5A, N indicates thenumber of input pixels. For example, selection of a transform type fromamong the plurality of transform types may depend on a prediction type(one of intra prediction and inter prediction), and may depend on anintra prediction mode.

Information indicating whether to apply such EMT or AMT (referred to as,for example, an EMT flag or an AMT flag) and information indicating theselected transform type is normally signaled at the CU level. It is tobe noted that the signaling of such information does not necessarilyneed to be performed at the CU level, and may be performed at anotherlevel (for example, at the bit sequence level, picture level, slicelevel, tile level, or CTU level).

In addition, transformer 106 may re-transform the transform coefficients(transform result). Such re-transform is also referred to as adaptivesecondary transform (AST) or non-separable secondary transform (NSST).For example, transformer 106 performs re-transform in units of asub-block (for example, 4×4 sub-block) included in a transformcoefficient block corresponding to an intra prediction error.Information indicating whether to apply NSST and information related toa transform matrix for use in NSST are normally signaled at the CUlevel. It is to be noted that the signaling of such information does notnecessarily need to be performed at the CU level, and may be performedat another level (for example, at the sequence level, picture level,slice level, tile level, or CTU level).

Transformer 106 may employ a separable transform and a non-separabletransform. A separable transform is a method in which a transform isperformed a plurality of times by separately performing a transform foreach of a number of directions according to the number of dimensions ofinputs. A non-separable transform is a method of performing a collectivetransform in which two or more dimensions in multidimensional inputs arecollectively regarded as a single dimension.

In one example of a non-separable transform, when an input is a 4×4block, the 4×4 block is regarded as a single array including sixteenelements, and the transform applies a 16×16 transform matrix to thearray.

In another example of a non-separable transform, a 4×4 input block isregarded as a single array including sixteen elements, and then atransform (hypercube givens transform) in which givens revolution isperformed on the array a plurality of times may be performed.

In the transform in transformer 106, the types of bases to betransformed into the frequency domain according to regions in a CU canbe switched. Examples include spatially varying transforms (SVT). InSVT, as illustrated in FIG. 5B, CUs are split into two equal regionshorizontally or vertically, and only one of the regions is transformedinto the frequency domain. A transform basis type can be set for eachregion. For example, DST7 and DST8 are used. In this example, only oneof these two regions in the CU is transformed, and the other is nottransformed. However, both of these two regions may be transformed. Inaddition, the splitting method is not limited to the splitting into twoequal regions, and can be more flexible. For example, the CU may besplit into four equal regions, or information indicating splitting maybe encoded separately and be signaled in the same manner as the CUsplitting. It is to be noted that SVT is also referred to as sub-blocktransform (SBT).

[Quantizer]

Quantizer 108 quantizes the transform coefficients output fromtransformer 106. More specifically, quantizer 108 scans, in a determinedscanning order, the transform coefficients of the current block, andquantizes the scanned transform coefficients based on quantizationparameters (QP) corresponding to the transform coefficients. Quantizer108 then outputs the quantized transform coefficients (hereinafter alsoreferred to as quantized coefficients) of the current block to entropyencoder 110 and inverse quantizer 112. The determined scanning order maybe predetermined.

A determined scanning order is an order for quantizing/inversequantizing transform coefficients. For example, a determined scanningorder may be defined as ascending order of frequency (from low to highfrequency) or descending order of frequency (from high to lowfrequency).

A quantization parameter (QP) is a parameter defining a quantizationstep (quantization width). For example, when the value of thequantization parameter increases, the quantization step also increases.In other words, when the value of the quantization parameter increases,the quantization error increases.

In addition, a quantization matrix may be used for quantization. Forexample, several kinds of quantization matrices may be usedcorrespondingly to frequency transform sizes such as 4×4 and 8×8,prediction modes such as intra prediction and inter prediction, andpixel components such as luma and chroma pixel components. It is to benoted that quantization means digitalizing values sampled at determinedintervals correspondingly to determined levels. In this technical field,quantization may be referred to using other expressions, such asrounding and scaling, and may employ rounding and scaling. Thedetermined intervals and levels may be predetermined.

Methods using quantization matrices include a method using aquantization matrix which has been set directly at the encoder side anda method using a quantization matrix which has been set as a default(default matrix). At the encoder side, a quantization matrix suitablefor features of an image can be set by directly setting a quantizationmatrix. This case, however, has a disadvantage of increasing a codingamount for encoding the quantization matrix.

There is a method for quantizing a high-frequency coefficient and alow-frequency coefficient without using a quantization matrix. It is tobe noted that this method is equivalent to a method using a quantizationmatrix (flat matrix) whose coefficients have the same value.

The quantization matrix may be specified using, for example, a sequenceparameter set (SPS) or a picture parameter set (PPS). The SPS includes aparameter which is used for a sequence, and the PPS includes a parameterwhich is used for a picture. Each of the SPS and the PPS may be simplyreferred to as a parameter set.

[Entropy Encoder]

Entropy encoder 110 generates an encoded signal (encoded bitstream)based on quantized coefficients which have been input from quantizer108. More specifically, entropy encoder 110, for example, binarizesquantized coefficients, and arithmetically encodes the binary signal,and outputs a compressed bit stream or sequence.

[Inverse Quantizer]

Inverse quantizer 112 inverse quantizes quantized coefficients whichhave been input from quantizer 108. More specifically, inverse quantizer112 inverse quantizes, in a determined scanning order, quantizedcoefficients of the current block. Inverse quantizer 112 then outputsthe inverse quantized transform coefficients of the current block toinverse transformer 114. The determined scanning order may bepredetermined.

[Inverse Transformer]

Inverse transformer 114 restores prediction errors (residuals) byinverse transforming transform coefficients which have been input frominverse quantizer 112. More specifically, inverse transformer 114restores the prediction errors of the current block by applying aninverse transform corresponding to the transform applied by transformer106 on the transform coefficients. Inverse transformer 114 then outputsthe restored prediction errors to adder 116.

It is to be noted that since information is lost in quantization, therestored prediction errors do not match the prediction errors calculatedby subtractor 104. In other words, the restored prediction errorsnormally include quantization errors.

[Adder]

Adder 116 reconstructs the current block by adding prediction errorswhich have been input from inverse transformer 114 and predictionsamples which have been input from prediction controller 128. Adder 116then outputs the reconstructed block to block memory 118 and loop filter120. A reconstructed block is also referred to as a local decoded block.

[Block Memory]

Block memory 118 is, for example, storage for storing blocks in apicture to be encoded (hereinafter referred to as a current picture)which is referred to in intra prediction. More specifically, blockmemory 118 stores reconstructed blocks output from adder 116.

[Frame Memory]

Frame memory 122 is, for example, storage for storing reference picturesfor use in inter prediction, and is also referred to as a frame buffer.More specifically, frame memory 122 stores reconstructed blocks filteredby loop filter 120.

[Loop Filter]

Loop filter 120 applies a loop filter to blocks reconstructed by adder116, and outputs the filtered reconstructed blocks to frame memory 122.A loop filter is a filter used in an encoding loop (in-loop filter), andincludes, for example, a deblocking filter (DF or DBF), a sampleadaptive offset (SAO), and an adaptive loop filter (ALF).

In an ALF, a least square error filter for removing compressionartifacts is applied. For example, one filter selected from among aplurality of filters based on the direction and activity of localgradients is applied for each of 2×2 sub-blocks in the current block.

More specifically, first, each sub-block (for example, each 2×2sub-block) is categorized into one out of a plurality of classes (forexample, fifteen or twenty-five classes). The classification of thesub-block is based on gradient directionality and activity. For example,classification index C (for example, C=5D+A) is derived based ongradient directionality D (for example, 0 to 2 or 0 to 4) and gradientactivity A (for example, 0 to 4). Then, based on classification index C,each sub-block is categorized into one out of a plurality of classes.

For example, gradient directionality D is calculated by comparinggradients of a plurality of directions (for example, the horizontal,vertical, and two diagonal directions). Moreover, for example, gradientactivity A is calculated by adding gradients of a plurality ofdirections and quantizing the result of addition.

The filter to be used for each sub-block is determined from among theplurality of filters based on the result of such categorization.

The filter shape to be used in an ALF is, for example, a circularsymmetric filter shape. FIG. 6A through FIG. 6C illustrate examples offilter shapes used in ALFs. FIG. 6A illustrates a 5×5 diamond shapefilter, FIG. 6B illustrates a 7×7 diamond shape filter, and FIG. 6Cillustrates a 9×9 diamond shape filter. Information indicating thefilter shape is normally signaled at the picture level. It is to benoted that the signaling of such information indicating the filter shapedoes not necessarily need to be performed at the picture level, and maybe performed at another level (for example, at the sequence level, slicelevel, tile level, CTU level, or CU level).

The ON or OFF of the ALF is determined, for example, at the picturelevel or CU level. For example, the decision of whether to apply the ALFto luma may be made at the CU level, and the decision of whether toapply ALF to chroma may be made at the picture level. Informationindicating ON or OFF of the ALF is normally signaled at the picturelevel or CU level. It is to be noted that the signaling of informationindicating ON or OFF of the ALF does not necessarily need to beperformed at the picture level or CU level, and may be performed atanother level (for example, at the sequence level, slice level, tilelevel, or CTU level).

The coefficient set for the plurality of selectable filters (forexample, fifteen or up to twenty-five filters) is normally signaled atthe picture level. It is to be noted that the signaling of thecoefficient set does not necessarily need to be performed at the picturelevel, and may be performed at another level (for example, at thesequence level, slice level, tile level, CTU level, CU level, orsub-block level).

[Loop Filter>Deblocking Filter]

In a deblocking filter, loop filter 120 performs a filter process on ablock boundary in a reconstructed image so as to reduce distortion whichoccurs at the block boundary.

FIG. 7 is a block diagram illustrating one example of a specificconfiguration of loop filter 120 which functions as a deblocking filter.

Loop filter 120 includes: boundary determiner 1201; filter determiner1203; filtering executor 1205; process determiner 1208; filtercharacteristic determiner 1207; and switches 1202, 1204, and 1206.

Boundary determiner 1201 determines whether a pixel to bedeblock-filtered (that is, a current pixel) is present around a blockboundary. Boundary determiner 1201 then outputs the determination resultto switch 1202 and processing determiner 1208.

In the case where boundary determiner 1201 has determined that a currentpixel is present around a block boundary, switch 1202 outputs anunfiltered image to switch 1204. In the opposite case where boundarydeterminer 1201 has determined that no current pixel is present around ablock boundary, switch 1202 outputs an unfiltered image to switch 1206.

Filter determiner 1203 determines whether to perform deblockingfiltering of the current pixel, based on the pixel value of at least onesurrounding pixel located around the current pixel. Filter determiner1203 then outputs the determination result to switch 1204 and processingdeterminer 1208.

In the case where filter determiner 1203 has determined to performdeblocking filtering of the current pixel, switch 1204 outputs theunfiltered image obtained through switch 1202 to filtering executor1205. In the opposite case were filter determiner 1203 has determinednot to perform deblocking filtering of the current pixel, switch 1204outputs the unfiltered image obtained through switch 1202 to switch1206.

When obtaining the unfiltered image through switches 1202 and 1204,filtering executor 1205 executes, for the current pixel, deblockingfiltering with the filter characteristic determined by filtercharacteristic determiner 1207. Filtering executor 1205 then outputs thefiltered pixel to switch 1206.

Under control by processing determiner 1208, switch 1206 selectivelyoutputs a pixel which has not been deblock-filtered and a pixel whichhas been deblock-filtered by filtering executor 1205.

Processing determiner 1208 controls switch 1206 based on the results ofdeterminations made by boundary determiner 1201 and filter determiner1203. In other words, processing determiner 1208 causes switch 1206 tooutput the pixel which has been deblock-filtered when boundarydeterminer 1201 has determined that the current pixel is present aroundthe block boundary and filter determiner 1203 has determined to performdeblocking filtering of the current pixel. In addition, other than theabove case, processing determiner 1208 causes switch 1206 to output thepixel which has not been deblock-filtered. A filtered image is outputfrom switch 1206 by repeating output of a pixel in this way.

FIG. 8 is a conceptual diagram indicating an example of a deblockingfilter having a symmetrical filtering characteristic with respect to ablock boundary.

In a deblocking filter process, one of two deblocking filters havingdifferent characteristics, that is, a strong filter and a weak filter isselected using pixel values and quantization parameters. In the case ofthe strong filter, pixels p0 to p2 and pixels q0 to q2 are presentacross a block boundary as illustrated in FIG. 8, the pixel values ofthe respective pixel q0 to q2 are changed to pixel values q′0 to q′2 byperforming, for example, computations according to the expressionsbelow.

q′0=(p1+2×p0+2×q0+2×q1+q2+4)/8

q′1=(p0+q0+q1+q2+2)/4

q′2=(p0+q0+q1+3×q2+2×q3+4)/8

It is to be noted that, in the above expressions, p0 to p2 and q0 to q2are the pixel values of respective pixels p0 to p2 and pixels q0 to q2.In addition, q3 is the pixel value of neighboring pixel q3 located atthe opposite side of pixel q2 with respect to the block boundary. Inaddition, in the right side of each of the expressions, coefficientswhich are multiplied with the respective pixel values of the pixels tobe used for deblocking filtering are filter coefficients.

Furthermore, in the deblocking filtering, clipping may be performed sothat the calculated pixel values are not set over a threshold value. Inthe clipping process, the pixel values calculated according to the aboveexpressions are clipped to a value obtained according to “a computationpixel value±2×a threshold value” using the threshold value determinedbased on a quantization parameter. In this way, it is possible toprevent excessive smoothing.

FIG. 9 is a conceptual diagram for illustrating a block boundary onwhich a deblocking filter process is performed. FIG. 10 is a conceptualdiagram indicating examples of Bs values.

The block boundary on which the deblocking filter process is performedis, for example, a boundary between prediction units (PU) having 8×8pixel blocks as illustrated in FIG. 9 or a boundary between transformunits (TU). The deblocking filter process may be performed in units offour rows or four columns. First, boundary strength (Bs) values aredetermined as indicated in FIG. 10 for block P and block Q illustratedin FIG. 9.

According to the Bs values in FIG. 10, whether to perform deblockingfilter processes of block boundaries belonging to the same image usingdifferent strengths is determined. The deblocking filter process for achroma signal is performed when a Bs value is 2. The deblocking filterprocess for a luma signal is performed when a Bs value is 1 or more anda determined condition is satisfied. The determined condition may bepredetermined. It is to be noted that conditions for determining Bsvalues are not limited to those indicated in FIG. 10, and a Bs value maybe determined based on another parameter.

[Prediction Processor (Intra Predictor, Inter Predictor, PredictionController)]

FIG. 11 is a flow chart illustrating one example of a process performedby the prediction processor of encoder 100. It is to be noted that theprediction processor includes all or part of the following constituentelements: intra predictor 124; inter predictor 126; and predictioncontroller 128.

The prediction processor generates a prediction image of a current block(Step Sb_1). This prediction image is also referred to as a predictionsignal or a prediction block. It is to be noted that the predictionsignal is, for example, an intra prediction signal or an interprediction signal. Specifically, the prediction processor generates theprediction image of the current block using a reconstructed image whichhas been already obtained through generation of a prediction block,generation of a difference block, generation of a coefficient block,restoring of a difference block, and generation of a decoded imageblock.

The reconstructed image may be, for example, an image in a referencepicture, or an image of an encoded block in a current picture which isthe picture including the current block. The encoded block in thecurrent picture is, for example, a neighboring block of the currentblock.

FIG. 12 is a flow chart illustrating another example of a processperformed by the prediction processor of encoder 100.

The prediction processor generates a prediction image using a firstmethod (Step Sc_1 a), generates a prediction image using a second method(Step Sc_1 b), and generates a prediction image using a third method(Step Sc_1 c). The first method, the second method, and the third methodmay be mutually different methods for generating a prediction image.Each of the first to third methods may be an inter prediction method, anintra prediction method, or another prediction method. Theabove-described reconstructed image may be used in these predictionmethods.

Next, the prediction processor selects any one of a plurality ofprediction methods generated in Steps Sc_1 a, Sc_1 b, and Sc_1 c (StepSc_2). The selection of the prediction image, that is selection of amethod or a mode for obtaining a final prediction image may be made bycalculating a cost for each of the generated prediction images and basedon the cost. Alternatively, the selection of the prediction image may bemade based on a parameter which is used in an encoding process. Encoder100 may transform information for identifying a selected predictionimage, a method, or a mode into an encoded signal (also referred to asan encoded bitstream). The information may be, for example, a flag orthe like. In this way, the decoder is capable of generating a predictionimage according to the method or the mode selected based on theinformation in encoder 100. It is to be noted that, in the exampleillustrated in FIG. 12, the prediction processor selects any of theprediction images after the prediction images are generated using therespective methods. However, the prediction processor may select amethod or a mode based on a parameter for use in the above-describedencoding process before generating prediction images, and may generate aprediction image according to the method or mode selected.

For example, the first method and the second method may be intraprediction and inter prediction, respectively, and the predictionprocessor may select a final prediction image for a current block fromprediction images generated according to the prediction methods.

FIG. 13 is a flow chart illustrating another example of a processperformed by the prediction processor of encoder 100.

First, the prediction processor generates a prediction image using intraprediction (Step Sd_1 a), and generates a prediction image using interprediction (Step Sd_1 b). It is to be noted that the prediction imagegenerated by intra prediction is also referred to as an intra predictionimage, and the prediction image generated by inter prediction is alsoreferred to as an inter prediction image.

Next, the prediction processor evaluates each of the intra predictionimage and the inter prediction image (Step Sd_2). A cost may be used inthe evaluation. In other words, the prediction processor calculates costC for each of the intra prediction image and the inter prediction image.Cost C may be calculated according to an expression of an R-Doptimization model, for example, C=D+λ×R. In this expression, Dindicates a coding distortion of a prediction image, and is representedas, for example, a sum of absolute differences between the pixel valueof a current block and the pixel value of a prediction image. Inaddition. R indicates a predicted coding amount of a prediction image,specifically, the coding amount required to encode motion informationfor generating a prediction image, etc. In addition, λ indicates, forexample, a multiplier according to the method of Lagrange multiplier.

The prediction processor then selects the prediction image for which thesmallest cost C has been calculated among the intra prediction image andthe inter prediction image, as the final prediction image for thecurrent block (Step Sd_3). In other words, the prediction method or themode for generating the prediction image for the current block isselected.

[Intra Predictor]

Intra predictor 124 generates a prediction signal (intra predictionsignal) by performing intra prediction (also referred to as intra frameprediction) of the current block by referring to a block or blocks inthe current picture and stored in block memory 118. More specifically,intra predictor 124 generates an intra prediction signal by performingintra prediction by referring to samples (for example, luma and/orchroma values) of a block or blocks neighboring the current block, andthen outputs the intra prediction signal to prediction controller 128.

For example, intra predictor 124 performs intra prediction by using onemode from among a plurality of intra prediction modes which have beendefined. The intra prediction modes include one or more non-directionalprediction modes and a plurality of directional prediction modes. Thedefined modes may be predefined.

The one or more non-directional prediction modes include, for example,the planar prediction mode and DC prediction mode defined in theH.265/high-efficiency video coding (HEVC) standard.

The plurality of directional prediction modes include, for example, thethirty-three directional prediction modes defined in the H.265/HEVCstandard. It is to be noted that the plurality of directional predictionmodes may further include thirty-two directional prediction modes inaddition to the thirty-three directional prediction modes (for a totalof sixty-five directional prediction modes). FIG. 14 is a conceptualdiagram illustrating sixty-seven intra prediction modes in total thatmay be used in intra prediction (two non-directional prediction modesand sixty-five directional prediction modes). The solid arrows representthe thirty-three directions defined in the H.265/HEVC standard, and thedashed arrows represent the additional thirty-two directions (the twonon-directional prediction modes are not illustrated in FIG. 14).

In various kinds of processing examples, a luma block may be referred toin intra prediction of a chroma block. In other words, a chromacomponent of the current block may be predicted based on a lumacomponent of the current block. Such intra prediction is also referredto as cross-component linear model (CCLM) prediction. The intraprediction mode for a chroma block in which such a luma block isreferred to (also referred to as, for example, a CCLM mode) may be addedas one of the intra prediction modes for chroma blocks.

Intra predictor 124 may correct intra-predicted pixel values based onhorizontal/vertical reference pixel gradients. Intra predictionaccompanied by this sort of correcting is also referred to as positiondependent intra prediction combination (PDPC). Information indicatingwhether to apply PDPC (referred to as, for example, a PDPC flag) isnormally signaled at the CU level. It is to be noted that the signalingof such information does not necessarily need to be performed at the CUlevel, and may be performed at another level (for example, at thesequence level, picture level, slice level, tile level, or CTU level).

[Inter Predictor]

Inter predictor 126 generates a prediction signal (inter predictionsignal) by performing inter prediction (also referred to as inter frameprediction) of the current block by referring to a block or blocks in areference picture, which is different from the current picture and isstored in frame memory 122. Inter prediction is performed in units of acurrent block or a current sub-block (for example, a 4×4 block) in thecurrent block. For example, inter predictor 126 performs motionestimation in a reference picture for the current block or the currentsub-block, and finds out a reference block or a sub-block which bestmatches the current block or the current sub-block. Inter predictor 126then obtains motion information (for example, a motion vector) whichcompensates a motion or a change from the reference block or thesub-block to the current block or the sub-block. Inter predictor 126generates an inter prediction signal of the current block or thesub-block by performing motion compensation (or motion prediction) basedon the motion information. Inter predictor 126 outputs the generatedinter prediction signal to prediction controller 128.

The motion information used in motion compensation may be signaled asinter prediction signals in various forms. For example, a motion vectormay be signaled. As another example, the difference between a motionvector and a motion vector predictor may be signaled.

[Basic Flow of Inter Prediction]

FIG. 15 is a flow chart illustrating an example basic processing flow ofinter prediction.

First, inter predictor 126 generates a prediction signal (Steps Se_1 toSe_3). Next, subtractor 104 generates the difference between a currentblock and a prediction image as a prediction residual (Step Se_4).

Here, in the generation of the prediction image, inter predictor 126generates the prediction image through determination of a motion vector(MV) of the current block (Steps Se_1 and Se_2) and motion compensation(Step Se_3). Furthermore, in determination of an MV, inter predictor 126determines the MV through selection of a motion vector candidate (MVcandidate) (Step Se_1) and derivation of an MV (Step Se_2). Theselection of the MV candidate is made by, for example, selecting atleast one MV candidate from an MV candidate list. Alternatively, inderivation of an MV, inter predictor 126 may further select at least oneMV candidate from the at least one MV candidate, and determine theselected at least one MV candidate as the MV for the current block.Alternatively, inter predictor 126 may determine the MV for the currentblock by performing estimation in a reference picture region specifiedby each of the selected at least one MV candidate. It is to be notedthat the estimation in a reference picture region may be referred to asmotion estimation.

In addition, although Steps Se_1 to Se_3 are performed by interpredictor 126 in the above-described example, a process that is forexample Step Se_1, Step Se_2, or the like may be performed by anotherconstituent element included in encoder 100.

[Motion Vector Derivation Flow]

FIG. 16 is a flow chart illustrating one example of derivation of motionvectors.

Inter predictor 126 derives an MV of a current block in a mode forencoding motion information (for example, an MV). In this case, forexample, the motion information is encoded as a prediction parameter,and is signaled. In other words, the encoded motion information isincluded in an encoded signal (also referred to as an encodedbitstream).

Alternatively, inter predictor 126 derives an MV in a mode in whichmotion information is not encoded. In this case, no motion informationis included in an encoded signal.

Here. MV derivation modes may include a normal inter mode, a merge mode,a FRUC mode, an affine mode, etc. which are described later. Modes inwhich motion information is encoded among the modes include the normalinter mode, the merge mode, the affine mode (specifically, an affineinter mode and an affine merge mode), etc. It is to be noted that motioninformation may include not only an MV but also motion vector predictorselection information which is described later. Modes in which no motioninformation is encoded include the FRUC mode, etc. Inter predictor 126selects a mode for deriving an MV of the current block from the modes,and derives the MV of the current block using the selected mode.

FIG. 17 is a flow chart illustrating another example of derivation ofmotion vectors.

Inter predictor 126 derives an MV of a current block in a mode in whichan MV difference is encoded. In this case, for example, the MVdifference is encoded as a prediction parameter, and is signaled. Inother words, the encoded MV difference is included in an encoded signal.The MV difference is the difference between the MV of the current blockand the MV predictor.

Alternatively, inter predictor 126 derives an MV in a mode in which noMV difference is encoded. In this case, no encoded MV difference isincluded in an encoded signal.

Here, as described above, the MV derivation modes include the normalinter mode, the merge mode, the FRUC mode, the affine mode, etc. whichare described later. Modes in which an MV difference is encoded amongthe modes include the normal inter mode, the affine mode (specifically,the affine inter mode), etc. Modes in which no MV difference is encodedinclude the FRUC mode, the merge mode, the affine mode (specifically,the affine merge mode), etc. Inter predictor 126 selects a mode forderiving an MV of the current block from the plurality of modes, andderives the MV of the current block using the selected mode.

[Motion Vector Derivation Flow]

FIG. 18 is a flow chart illustrating another example of derivation ofmotion vectors. The MV derivation modes which are inter prediction modesinclude a plurality of modes and are roughly divided into modes in whichan MV difference is encoded and modes in which no motion vectordifference is encoded. The modes in which no MV difference is encodedinclude the merge mode, the FRUC mode, the affine mode (specifically,the affine merge mode), etc. These modes are described in detail later.Simply, the merge mode is a mode for deriving an MV of a current blockby selecting a motion vector from an encoded surrounding block, and theFRUC mode is a mode for deriving an MV of a current block by performingestimation between encoded regions. The affine mode is a mode forderiving, as an MV of a current block, a motion vector of each of aplurality of sub-blocks included in the current block, assuming affinetransform.

More specifically, as illustrated when the inter prediction modeinformation indicates 0 (0 in Sf_1), inter predictor 126 derives amotion vector using the merge mode (Sf_2). When the inter predictionmode information indicates 1 (1 in Sf_1), inter predictor 126 derives amotion vector using the FRUC mode (Sf_3). When the inter prediction modeinformation indicates 2 (2 in Sf_1), inter predictor 126 derives amotion vector using the affine mode (specifically, the affine mergemode) (Sf_4). When the inter prediction mode information indicates 3 (3in Sf_1), inter predictor 126 derives a motion vector using a mode inwhich an MV difference is encoded (for example, a normal inter mode(Sf_5).

[MV Derivation>Normal Inter Mode]

The normal inter mode is an inter prediction mode for deriving an MV ofa current block based on a block similar to the image of the currentblock from a reference picture region specified by an MV candidate. Inthis normal inter mode, an MV difference is encoded.

FIG. 19 is a flow chart illustrating an example of inter prediction innormal inter mode.

First, inter predictor 126 obtains a plurality of MV candidates for acurrent block based on information such as MVs of a plurality of encodedblocks temporally or spatially surrounding the current block (StepSg_1). In other words, inter predictor 126 generates an MV candidatelist.

Next, inter predictor 126 extracts N (an integer of 2 or larger) MVcandidates from the plurality of MV candidates obtained in Step Sg_1, asmotion vector predictor candidates (also referred to as MV predictorcandidates) according to a determined priority order (Step Sg_2). It isto be noted that the priority order may be determined in advance foreach of the N MV candidates.

Next, inter predictor 126 selects one motion vector predictor candidatefrom the N motion vector predictor candidates, as the motion vectorpredictor (also referred to as an MV predictor) of the current block(Step Sg_3). At this time, inter predictor 126 encodes, in a stream,motion vector predictor selection information for identifying theselected motion vector predictor. It is to be noted that the stream isan encoded signal or an encoded bitstream as described above.

Next, inter predictor 126 derives an MV of a current block by referringto an encoded reference picture (Step Sg_4). At this time, interpredictor 126 further encodes, in the stream, the difference valuebetween the derived MV and the motion vector predictor as an MVdifference. It is to be noted that the encoded reference picture is apicture including a plurality of blocks which have been reconstructedafter being encoded.

Lastly, inter predictor 126 generates a prediction image for the currentblock by performing motion compensation of the current block using thederived MV and the encoded reference picture (Step Sg_5). It is to benoted that the prediction image is an inter prediction signal asdescribed above.

In addition, information indicating the inter prediction mode (normalinter mode in the above example) used to generate the prediction imageis, for example, encoded as a prediction parameter.

It is to be noted that the MV candidate list may be also used as a listfor use in another mode. In addition, the processes related to the MVcandidate list may be applied to processes related to the list for usein another mode. The processes related to the MV candidate list include,for example, extraction or selection of an MV candidate from the MVcandidate list, reordering of MV candidates, or deletion of an MVcandidate.

[MV Derivation>Merge Mode]

The merge mode is an inter prediction mode for selecting an MV candidatefrom an MV candidate list as an MV of a current block, thereby derivingthe MV.

FIG. 20 is a flow chart illustrating an example of inter prediction inmerge mode.

First, inter predictor 126 obtains a plurality of MV candidates for acurrent block based on information such as MVs of a plurality of encodedblocks temporally or spatially surrounding the current block (StepSh_1). In other words, inter predictor 126 generates an MV candidatelist.

Next, inter predictor 126 selects one MV candidate from the plurality ofMV candidates obtained in Step Sh_1, thereby deriving an MV of thecurrent block (Step Sh_2). At this time, inter predictor 126 encodes, ina stream, MV selection information for identifying the selected MVcandidate.

Lastly, inter predictor 126 generates a prediction image for the currentblock by performing motion compensation of the current block using thederived MV and the encoded reference picture (Step Sh_3).

In addition, information indicating the inter prediction mode (mergemode in the above example) used to generate the prediction image andincluded in the encoded signal is, for example, encoded as a predictionparameter.

FIG. 21 is a conceptual diagram for illustrating one example of a motionvector derivation process of a current picture in merge mode.

First, an MV candidate list in which MV predictor candidates areregistered is generated. Examples of MV predictor candidates include:spatially neighboring MV predictors which are MVs of a plurality ofencoded blocks located spatially surrounding a current block; temporallyneighboring MV predictors which are MVs of surrounding blocks on whichthe position of a current block in an encoded reference picture isprojected; combined MV predictors which are MVs generated by combiningthe MV value of a spatially neighboring MV predictor and the MV of atemporally neighboring MV predictor; and a zero MV predictor which is anMV having a zero value.

Next, one MV predictor is selected from a plurality of MV predictorsregistered in an MV predictor list, and the selected MV predictor isdetermined as the MV of a current block.

Furthermore, the variable length encoder describes and encodes, in astream, merge_idx which is a signal indicating which MV predictor hasbeen selected.

It is to be noted that the MV predictors registered in the MV predictorlist described in FIG. 21 are examples. The number of MV predictors maybe different from the number of MV predictors in the diagram, the MVpredictor list may be configured in such a manner that some of the kindsof the MV predictors in the diagram may not be included, or that one ormore MV predictors other than the kinds of MV predictors in the diagramare included.

A final MV may be determined by performing a decoder motion vectorrefinement process (DMVR) to be described later using the MV of thecurrent block derived in merge mode.

It is to be noted that the MV predictor candidates are MV candidatesdescribed above, and the MV predictor list is the MV candidate listdescribed above. It is to be noted that the MV candidate list may bereferred to as a candidate list. In addition, merge_idx is MV selectioninformation.

[MV Derivation>FRUC Mode]

Motion information may be derived at the decoder side without beingsignaled from the encoder side. It is to be noted that, as describedabove, the merge mode defined in the H.265/HEVC standard may be used. Inaddition, for example, motion information may be derived by performingmotion estimation at the decoder side. In an embodiment, at the decoderside, motion estimation is performed without using any pixel value in acurrent block.

Here, a mode for performing motion estimation at the decoder side isdescribed. The mode for performing motion estimation at the decoder sidemay be referred to as a pattern matched motion vector derivation (PMMVD)mode, or a frame rate up-conversion (FRUC) mode.

One example of a FRUC process in the form of a flow chart is illustratedin FIG. 22. First, a list of a plurality of candidates each having amotion vector (MV) predictor (that is, an MV candidate list that may bealso used as a merge list) is generated by referring to a motion vectorin an encoded block which spatially or temporally neighbors a currentblock (Step Si_1). Next, a best MV candidate is selected from theplurality of MV candidates registered in the MV candidate list (StepSi_2). For example, the evaluation values of the respective MVcandidates included in the MV candidate list are calculated, and one MVcandidate is selected based on the evaluation values. Based on theselected motion vector candidates, a motion vector for the current blockis then derived (Step Si_4). More specifically, for example, theselected motion vector candidate (best MV candidate) is derived directlyas the motion vector for the current block. In addition, for example,the motion vector for the current block may be derived using patternmatching in a surrounding region of a position in a reference picturewhere the position in the reference picture corresponds to the selectedmotion vector candidate. In other words, estimation using the patternmatching and the evaluation values may be performed in the surroundingregion of the best MV candidate, and when there is an MV that yields abetter evaluation value, the best MV candidate may be updated to the MVthat yields the better evaluation value, and the updated MV may bedetermined as the final MV for the current block. A configuration inwhich no such a process for updating the best MV candidate to the MVhaving a better evaluation value is performed is also possible.

Lastly, inter predictor 126 generates a prediction image for the currentblock by performing motion compensation of the current block using thederived MV and the encoded reference picture (Step Si_5).

A similar process may be performed in units of a sub-block.

Evaluation values may be calculated according to various kinds ofmethods. For example, a comparison is made between a reconstructed imagein a region in a reference picture corresponding to a motion vector anda reconstructed image in a determined region (the region may be, forexample, a region in another reference picture or a region in aneighboring block of a current picture, as indicated below). Thedetermined region may be predetermined.

The difference between the pixel values of the two reconstructed imagesmay be used for an evaluation value of the motion vectors. It is to benoted that an evaluation value may be calculated using information otherthan the value of the difference.

Next, an example of pattern matching is described in detail. First, oneMV candidate included in an MV candidate list (for example, a mergelist) is selected as a start point of estimation by the patternmatching. For example, as the pattern matching, either a first patternmatching or a second pattern matching may be used. The first patternmatching and the second pattern matching are also referred to asbilateral matching and template matching, respectively.

[MV Derivation>FRUC>Bilateral Matching]

In the first pattern matching, pattern matching is performed between twoblocks along a motion trajectory of a current block which are two blocksin different two reference pictures. Accordingly, in the first patternmatching, a region in another reference picture along the motiontrajectory of the current block is used as a determined region forcalculating the evaluation value of the above-described candidate. Thedetermined region may be predetermined.

FIG. 23 is a conceptual diagram for illustrating one example of thefirst pattern matching (bilateral matching) between the two blocks inthe two reference pictures along the motion trajectory. As illustratedin FIG. 23, in the first pattern matching, two motion vectors (MV0, MV1)are derived by estimating a pair which best matches among pairs in thetwo blocks in the two different reference pictures (Ref0, Ref1) whichare the two blocks along the motion trajectory of the current block (Curblock). More specifically, a difference between the reconstructed imageat a specified location in the first encoded reference picture (Ref0)specified by an MV candidate and the reconstructed image at a specifiedlocation in the second encoded reference picture (Ref1) specified by asymmetrical MV obtained by scaling the MV candidate at a display timeinterval is derived for the current block, and an evaluation value iscalculated using the value of the obtained difference. It is possible toselect, as the final MV, the MV candidate which yields the bestevaluation value among the plurality of MV candidates, and which islikely to produce good results.

In the assumption of a continuous motion trajectory, the motion vectors(MV0, MV1) specifying the two reference blocks are proportional totemporal distances (TD0, TD1) between the current picture (Cur Pic) andthe two reference pictures (Ref0, Ref1). For example, when the currentpicture is temporally located between the two reference pictures and thetemporal distances from the current picture to the respective tworeference pictures are equal to each other, mirror-symmetricalbi-directional motion vectors are derived in the first pattern matching.

[MV Derivation>FRUC>Template Matching]

In the second pattern matching (template matching), pattern matching isperformed between a block in a reference picture and a template in thecurrent picture (the template is a block neighboring the current blockin the current picture (the neighboring block is, for example, an upperand/or left neighboring block(s))). Accordingly, in the second patternmatching, the block neighboring the current block in the current pictureis used as the determined region for calculating the evaluation value ofthe above-described candidate.

FIG. 24 is a conceptual diagram for illustrating one example of patternmatching (template matching) between a template in a current picture anda block in a reference picture. As illustrated in FIG. 24, in the secondpattern matching, the motion vector of the current block (Cur block) isderived by estimating, in the reference picture (Ref0), the block whichbest matches the block neighboring the current block in the currentpicture (Cur Pic). More specifically, it is possible that the differencebetween a reconstructed image in an encoded region which neighbors bothleft and above or either left or above and a reconstructed image whichis in a corresponding region in the encoded reference picture (Ref0) andis specified by an MV candidate is derived, an evaluation value iscalculated using the value of the obtained difference, and the MVcandidate which yields the best evaluation value among a plurality of MVcandidates is selected as the best MV candidate.

Such information indicating whether to apply the FRUC mode (referred toas, for example, a FRUC flag) may be signaled at the CU level. Inaddition, when the FRUC mode is applied (for example, when a FRUC flagis true), information indicating an applicable pattern matching method(either the first pattern matching or the second pattern matching) maybe signaled at the CU level. It is to be noted that the signaling ofsuch information does not necessarily need to be performed at the CUlevel, and may be performed at another level (for example, at thesequence level, picture level, slice level, tile level, CTU level, orsub-block level).

[MV Derivation>Affine Mode]

Next, the affine mode for deriving a motion vector in units of asub-block based on motion vectors of a plurality of neighboring blocksis described. This mode is also referred to as an affine motioncompensation prediction mode.

FIG. 25A is a conceptual diagram for illustrating one example ofderiving a motion vector of each sub-block based on motion vectors of aplurality of neighboring blocks. In FIG. 25A, the current block includessixteen 4×4 sub-blocks. Here, motion vector V₀ at an upper-left cornercontrol point in the current block is derived based on a motion vectorof a neighboring block, and likewise, motion vector V, at an upper-rightcorner control point in the current block is derived based on a motionvector of a neighboring sub-block. Two motion vectors v₀ and v₁ may beprojected according to an expression (1A) indicated below, and motionvectors (v_(x), v_(y)) for the respective sub-blocks in the currentblock may be derived.

[Math.  1] $\begin{matrix}\{ \begin{matrix}{v_{x} = {{\frac{( {v_{1x} - v_{0x}} )}{w}x} - {\frac{( {v_{1y} - v_{0y}} )}{w}y} + v_{0x}}} \\{v_{y} = {{\frac{( {v_{1y} - v_{0y}} )}{w}x} - {\frac{( {v_{1x} - v_{0x}} )}{w}y} + v_{0y}}}\end{matrix}  & ( {1A} )\end{matrix}$

Here, x and y indicate the horizontal position and the vertical positionof the sub-block, respectively, and w indicates a determined weightingcoefficient. The determined weighting coefficient may be predetermined.

Such information indicating the affine mode (for example, referred to asan affine flag) may be signaled at the CU level. It is to be noted thatthe signaling of the information indicating the affine mode does notnecessarily need to be performed at the CU level, and may be performedat another level (for example, at the sequence level, picture level,slice level, tile level, CTU level, or sub-block level).

In addition, the affine mode may include several modes for differentmethods for deriving motion vectors at the upper-left and upper-rightcorner control points. For example, the affine mode include two modeswhich are the affine inter mode (also referred to as an affine normalinter mode) and the affine merge mode.

[MV Derivation>Affine Mode]

FIG. 25B is a conceptual diagram for illustrating one example ofderiving a motion vector of each sub-block in affine mode in which threecontrol points are used. In FIG. 25B, the current block includes sixteen4×4 blocks. Here, motion vector V₀ at the upper-left corner controlpoint for the current block is derived based on a motion vector of aneighboring block, and likewise, motion vector V₁ at the upper-rightcorner control point for the current block is derived based on a motionvector of a neighboring block, and motion vector V₂ at the lower-leftcorner control point for the current block is derived based on a motionvector of a neighboring block. Three motion vectors v₀, v₁, and v₂ maybe projected according to an expression (1B) indicated below, and motionvectors (v_(x), v_(y)) for the respective sub-blocks in the currentblock may be derived.

[Math.  2] $\begin{matrix}\{ \begin{matrix}{v_{x} = {{\frac{( {v_{1x} - v_{0x}} )}{w}x} - {\frac{( {v_{2x} - v_{0x}} )}{h}y} + v_{0x}}} \\{v_{y} = {{\frac{( {v_{1y} - v_{0y}} )}{w}x} - {\frac{( {v_{2y} - v_{0y}} )}{h}y} + v_{0y}}}\end{matrix}  & ( {1B} )\end{matrix}$

Here, x and y indicate the horizontal position and the vertical positionof the center of the sub-block, respectively, w indicates the width ofthe current block, and h indicates the height of the current block.

Affine modes in which different numbers of control points (for example,two and three control points) are used may be switched and signaled atthe CU level. It is to be noted that information indicating the numberof control points in affine mode used at the CU level may be signaled atanother level (for example, the sequence level, picture level, slicelevel, tile level, CTU level, or sub-block level).

In addition, such an affine mode in which three control points are usedmay include different methods for deriving motion vectors at theupper-left, upper-right, and lower-left corner control points. Forexample, the affine modes include two modes which are the affine intermode (also referred to as the affine normal inter mode) and the affinemerge mode.

[MV Derivation>Affine Merge Mode]

FIG. 26A, FIG. 26B, and FIG. 26C are conceptual diagrams forillustrating the affine merge mode.

As illustrated in FIG. 26A, in the affine merge mode, for example,motion vector predictors at respective control points of a current blockare calculated based on a plurality of motion vectors corresponding toblocks encoded according to the affine mode among encoded block A(left), block B (upper), block C (upper-right), block D (lower-left),and block E (upper-left) which neighbor the current block. Morespecifically, encoded block A (left), block B (upper), block C(upper-right), block D (lower-left), and block E (upper-left) arechecked in the listed order, and the first effective block encodedaccording to the affine mode is identified. Motion vector predictors atthe control points of the current block are calculated based on aplurality of motion vectors corresponding to the identified block.

For example, as illustrated in FIG. 26B, when block A which neighbors tothe left of the current block has been encoded according to an affinemode in which two control points are used, motion vectors v₃ and v₄projected at the upper-left corner position and the upper-right cornerposition of the encoded block including block A are derived. Motionvector predictor v₀ at the upper-left corner control point of thecurrent block and motion vector predictor v₁ at the upper-right cornercontrol point of the current block are then calculated from derivedmotion vectors v₃ and v₄.

For example, as illustrated in FIG. 26C, when block A which neighbors tothe left of the current block has been encoded according to an affinemode in which three control points are used, motion vectors v₃, v₄, andv₅ projected at the upper-left corner position, the upper-right cornerposition, and the lower-left corner position of the encoded blockincluding block A are derived. Motion vector predictor v₀ at theupper-left corner control point of the current block, motion vectorpredictor v₁ at the upper-right corner control point of the currentblock, and motion vector predictor v₂ at the lower-left corner controlpoint of the current block are then calculated from derived motionvectors v₃, v₄, and v₅.

It is to be noted that this method for deriving motion vector predictorsmay be used to derive motion vector predictors of the respective controlpoints of the current block in Step Sj_1 in FIG. 29 described later.

FIG. 27 is a flow chart illustrating one example of the affine mergemode.

In affine merge mode as illustrated, first, inter predictor 126 derivesMV predictors of respective control points of a current block (StepSk_1). The control points are an upper-left corner point of the currentblock and an upper-right corner point of the current block asillustrated in FIG. 25A, or an upper-left corner point of the currentblock, an upper-right corner point of the current block, and alower-left corner point of the current block as illustrated in FIG. 25B.

In other words, as illustrated in FIG. 26A, inter predictor 126 checksencoded block A (left), block B (upper), block C (upper-right), block D(lower-left), and block E (upper-left) in the listed order, andidentifies the first effective block encoded according to the affinemode.

When block A is identified and block A has two control points, asillustrated in FIG. 26B, inter predictor 126 calculates motion vector v₀at the upper-left corner control point of the current block and motionvector v₁ at the upper-right corner control point of the current blockfrom motion vectors v₃ and v₄ at the upper-left corner and theupper-right corner of the encoded block including block A. For example,inter predictor 126 calculates motion vector v₀ at the upper-left cornercontrol point of the current block and motion vector v₁ at theupper-right corner control point of the current block by projectingmotion vectors v₃ and v₄ at the upper-left corner and the upper-rightcorner of the encoded block onto the current block.

Alternatively, when block A is identified and block A has three controlpoints, as illustrated in FIG. 26C, inter predictor 126 calculatesmotion vector v₀ at the upper-left corner control point of the currentblock, motion vector v₁ at the upper-right corner control point of thecurrent block, and motion vector v₂ at the lower-left corner controlpoint of the current block from motion vectors v₃, v₄, and v₅ at theupper-left corner, the upper-right corner, and the lower-left corner ofthe encoded block including block A. For example, inter predictor 126calculates motion vector v₀ at the upper-left corner control point ofthe current block, motion vector v₁ at the upper-right corner controlpoint of the current block, and motion vector v₂ at the lower-leftcorner control point of the current block by projecting motion vectorsv₃, v₄, and v₅ at the upper-left corner, the upper-right corner, and thelower-left corner of the encoded block onto the current block.

Next, inter predictor 126 performs motion compensation of each of aplurality of sub-blocks included in the current block. In other words,inter predictor 126 calculates, for each of the plurality of sub-blocks,a motion vector of the sub-block as an affine MV, by using either (i)two motion vector predictors v₀ and v₁ and the expression (1A) describedabove or (ii) three motion vector predictors v₀, v₁, and v₂ and theexpression (1B) described above (Step Sk_2). Inter predictor 126 thenperforms motion compensation of the sub-blocks using these affine MVsand encoded reference pictures (Step Sk_3). As a result, motioncompensation of the current block is performed to generate a predictionimage of the current block.

[MV Derivation>Affine Inter Mode]

FIG. 28A is a conceptual diagram for illustrating an affine inter modein which two control points are used.

In the affine inter mode, as illustrated in FIG. 28A, a motion vectorselected from motion vectors of encoded block A, block B, and block Cwhich neighbor the current block is used as motion vector predictor v₀at the upper-left corner control point of the current block. Likewise, amotion vector selected from motion vectors of encoded block D and blockE which neighbor the current block is used as motion vector predictor v₁at the upper-right corner control point of the current block.

FIG. 28B is a conceptual diagram for illustrating an affine inter modein which three control points are used.

In the affine inter mode, as illustrated in FIG. 28B, a motion vectorselected from motion vectors of encoded block A, block B, and block Cwhich neighbor the current block is used as motion vector predictor v₀at the upper-left corner control point of the current block. Likewise, amotion vector selected from motion vectors of encoded block D and blockE which neighbor the current block is used as motion vector predictor v₁at the upper-right corner control point of the current block.Furthermore, a motion vector selected from motion vectors of encodedblock F and block G which neighbor the current block is used as motionvector predictor v₂ at the lower-left corner control point of thecurrent block.

FIG. 29 is a flow chart illustrating one example of an affine intermode.

In the affine inter mode as illustrated, first, inter predictor 126derives MV predictors (v₀, v₁) or (v₀, v₁, v₂) of respective two orthree control points of a current block (Step Sj_1). The control pointsare an upper-left corner point of the current block and an upper-rightcorner point of the current block as illustrated in FIG. 25A, or anupper-left corner point of the current block, an upper-right cornerpoint of the current block, and a lower-left corner point of the currentblock as illustrated in FIG. 25B.

In other words, inter predictor 126 derives the motion vector predictors(v₀, v₁) or (v₀, v₁, v₂) of respective two or three control points ofthe current block by selecting motion vectors of any of the blocks amongencoded blocks in the vicinity of the respective control points of thecurrent block illustrated in either FIG. 28A or FIG. 28B. At this time,inter predictor 126 encodes, in a stream, motion vector predictorselection information for identifying the selected two motion vectors.

For example, inter predictor 126 may determine, using a cost evaluationor the like, the block from which a motion vector as a motion vectorpredictor at a control point is selected from among encoded blocksneighboring the current block, and may describe, in a bitstream, a flagindicating which motion vector predictor has been selected.

Next, inter predictor 126 performs motion estimation (Step Sj_3 andSj_4) while updating a motion vector predictor selected or derived inStep Sj_1 (Step Sj_2). In other words, inter predictor 126 calculates,as an affine MV, a motion vector of each of sub-blocks which correspondsto an updated motion vector predictor, using either the expression (1A)or expression (1B) described above (Step Sj_3). Inter predictor 126 thenperforms motion compensation of the sub-blocks using these affine MVsand encoded reference pictures (Step Sj_4). As a result, for example,inter predictor 126 determines the motion vector predictor which yieldsthe smallest cost as the motion vector at a control point in a motionestimation loop (Step Sj_5). At this time, inter predictor 126 furtherencodes, in the stream, the difference value between the determined MVand the motion vector predictor as an MV difference.

Lastly, inter predictor 126 generates a prediction image for the currentblock by performing motion compensation of the current block using thedetermined MV and the encoded reference picture (Step Sj_6).

[MV Derivation>Affine Inter Mode]

When affine modes in which different numbers of control points (forexample, two and three control points) are used may be switched andsignaled at the CU level, the number of control points in an encodedblock and the number of control points in a current block may bedifferent from each other. FIG. 30A and FIG. 30B are conceptual diagramsfor illustrating methods for deriving motion vector predictors atcontrol points when the number of control points in an encoded block andthe number of control points in a current block are different from eachother.

For example, as illustrated in FIG. 30A, when a current block has threecontrol points at the upper-left corner, the upper-right corner, and thelower-left corner, and block A which neighbors to the left of thecurrent block has been encoded according to an affine mode in which twocontrol points are used, motion vectors v₃ and v₄ projected at theupper-left corner position and the upper-right corner position in theencoded block including block A are derived. Motion vector predictor v₀at the upper-left corner control point of the current block and motionvector predictor v₁ at the upper-right corner control point of thecurrent block are then calculated from derived motion vectors v₃ and v₄.Furthermore, motion vector predictor v₂ at the lower-left corner controlpoint is calculated from derived motion vectors v₀ and v₁.

For example, as illustrated in FIG. 30B, when a current block has twocontrol points at the upper-left corner and the upper-right corner, andblock A which neighbors to the left of the current block has beenencoded according to the affine mode in which three control points areused, motion vectors v₃, v₄, and v₅ projected at the upper-left cornerposition, the upper-right corner position, and the lower-left cornerposition in the encoded block including block A are derived. Motionvector predictor v₀ at the upper-left corner control point of thecurrent block and motion vector predictor v₁ at the upper-right cornercontrol point of the current block are then calculated from derivedmotion vectors v₃, v₄, and v₅.

It is to be noted that this method for deriving motion vector predictorsmay be used to derive motion vector predictors of the respective controlpoints of the current block in Step Sj_1 in FIG. 29.

[MV Derivation>DMVR]

FIG. 31A is a flow chart illustrating a relationship between the mergemode and DMVR.

Inter predictor 126 derives a motion vector of a current block accordingto the merge mode (Step Sl_1). Next, inter predictor 126 determineswhether to perform estimation of a motion vector, that is, motionestimation (Step Sl_2). Here, when determining not to perform motionestimation (No in Step Sl_2), inter predictor 126 determines the motionvector derived in Step Sl_1 as the final motion vector for the currentblock (Step Sl_4). In other words, in this case, the motion vector ofthe current block is determined according to the merge mode.

When determining to perform motion estimation in Step Sl_1 (Yes in StepSl_2), inter predictor 126 derives the final motion vector for thecurrent block by estimating a surrounding region of the referencepicture specified by the motion vector derived in Step Sl_1 (Step Sl_3).In other words, in this case, the motion vector of the current block isdetermined according to the DMVR.

FIG. 31B is a conceptual diagram for illustrating one example of a DMVRprocess for determining an MV.

First, (for example, in merge mode) the best MVP which has been set tothe current block is determined to be an MV candidate. A reference pixelis identified from a first reference picture (L0) which is an encodedpicture in the L0 direction according to an MV candidate (L0). Likewise,a reference pixel is identified from a second reference picture (L1)which is an encoded picture in the L1 direction according to an MVcandidate (L1). A template is generated by calculating an average ofthese reference pixels.

Next, each of the surrounding regions of MV candidates of the firstreference picture (L0) and the second reference picture (L1) areestimated, and the MV which yields the smallest cost is determined to bethe final MV. It is to be noted that the cost value may be calculated,for example, using a difference value between each of the pixel valuesin the template and a corresponding one of the pixel values in theestimation region, the values of MV candidates, etc.

It is to be noted that the processes, configurations, and operationsdescribed here typically are basically common between the encoder and adecoder to be described later.

Exactly the same example processes described here do not always need tobe performed. Any process for enabling derivation of the final MV byestimation in surrounding regions of MV candidates may be used.

[Motion Compensation>BIO/OBMC]

Motion compensation involves a mode for generating a prediction image,and correcting the prediction image. The mode is, for example, BIO andOBMC to be described later.

FIG. 32 is a flow chart illustrating one example of generation of aprediction image.

Inter predictor 126 generates a prediction image (Step Sm_1), andcorrects the prediction image, for example, according to any of themodes described above (Step Sm_2).

FIG. 33 is a flow chart illustrating another example of generation of aprediction image.

Inter predictor 126 determines a motion vector of a current block (StepSn_1). Next, inter predictor 126 generates a prediction image (StepSn_2), and determines whether to perform a correction process (StepSn_3). Here, when determining to perform a correction process (Yes inStep Sn_3), inter predictor 126 generates the final prediction image bycorrecting the prediction image (Step Sn_4). When determining not toperform a correction process (No in Step Sn_3), inter predictor 126outputs the prediction image as the final prediction image withoutcorrecting the prediction image (Step Sn_5).

In addition, motion compensation involves a mode for correcting aluminance of a prediction image when generating the prediction image.The mode is, for example, LIC to be described later.

FIG. 34 is a flow chart illustrating another example of generation of aprediction image.

Inter predictor 126 derives a motion vector of a current block (StepSo_1). Next, inter predictor 126 determines whether to perform aluminance correction process (Step So_2). Here, when determining toperform a luminance correction process (Yes in Step So_2), interpredictor 126 generates the prediction image while performing aluminance correction process (Step So_3). In other words, the predictionimage is generated using LIC. When determining not to perform aluminance correction process (No in Step So_2), inter predictor 126generates a prediction image by performing normal motion compensationwithout performing a luminance correction process (Step So_4).

[Motion Compensation>OBMC]

It is to be noted that an inter prediction signal may be generated usingmotion information for a neighboring block in addition to motioninformation for the current block obtained from motion estimation. Morespecifically, the inter prediction signal may be generated in units of asub-block in the current block by performing a weighted addition of aprediction signal based on motion information obtained from motionestimation (in the reference picture) and a prediction signal based onmotion information for a neighboring block (in the current picture).Such inter prediction (motion compensation) is also referred to asoverlapped block motion compensation (OBMC).

In OBMC mode, information indicating a sub-block size for OBMC (referredto as, for example, an OBMC block size) may be signaled at the sequencelevel. Moreover, information indicating whether to apply the OBMC mode(referred to as, for example, an OBMC flag) may be signaled at the CUlevel. It is to be noted that the signaling of such information does notnecessarily need to be performed at the sequence level and CU level, andmay be performed at another level (for example, at the picture level,slice level, tile level, CTU level, or sub-block level).

Examples of the OBMC mode will be described in further detail. FIGS. 35and 36 are a flow chart and a conceptual diagram for illustrating anoutline of a prediction image correction process performed by an OBMCprocess.

First, as illustrated in FIG. 36, a prediction image (Pred) is obtainedthrough normal motion compensation using a motion vector (MV) assignedto the processing target (current) block. In FIG. 36, the arrow “MV”points a reference picture, and indicates what the current block of thecurrent picture refers to in order to obtain a prediction image.

Next, a prediction image (Pred_L) is obtained by applying a motionvector (MV_L) which has been already derived for the encoded blockneighboring to the left of the current block to the current block(re-using the motion vector for the current block). The motion vector(MV_L) is indicated by an arrow “MV_L” indicating a reference picturefrom a current block. A first correction of a prediction image isperformed by overlapping two prediction images Pred and Pred_L. Thisprovides an effect of blending the boundary between neighboring blocks.

Likewise, a prediction image (Pred_U) is obtained by applying a motionvector (MV_U) which has been already derived for the encoded blockneighboring above the current block to the current block (re-using themotion vector for the current block). The motion vector (MV_U) isindicated by an arrow “MV_U” indicating a reference picture from acurrent block. A second correction of a prediction image is performed byoverlapping the prediction image Pred_U to the prediction images (forexample, Pred and Pred_L) on which the first correction has beenperformed. This provides an effect of blending the boundary betweenneighboring blocks. The prediction image obtained by the secondcorrection is the one in which the boundary between the neighboringblocks has been blended (smoothed), and thus is the final predictionimage of the current block.

Although the above example is a two-path correction method using leftand upper neighboring blocks, it is to be noted that the correctionmethod may be three- or more-path correction method using also the rightneighboring block and/or the lower neighboring block.

It is to be noted that the region in which such overlapping is performedmay be only part of a region near a block boundary instead of the pixelregion of the entire block.

It is to be noted that the prediction image correction process accordingto OBMC for obtaining one prediction image Pred from one referencepicture by overlapping additional prediction image Pred_L and Pred_Uhave been described above. However, when a prediction image is correctedbased on a plurality of reference images, a similar process may beapplied to each of the plurality of reference pictures. In such a case,after corrected prediction images are obtained from the respectivereference pictures by performing OBMC image correction based on theplurality of reference pictures, the obtained corrected predictionimages are further overlapped to obtain the final prediction image.

It is to be noted that, in OBMC, the unit of a current block may be theunit of a prediction block or the unit of a sub-block obtained byfurther splitting the prediction block.

One example of a method for determining whether to apply an OBMC processis a method for using an obmc_flag which is a signal indicating whetherto apply an OBMC process. As one specific example, an encoder determineswhether the current block belongs to a region having complicated motion.The encoder sets the obmc_flag to a value of “1” when the block belongsto a region having complicated motion and applies an OBMC process whenencoding, and sets the obmc_flag to a value of “0” when the block doesnot belong to a region having complicated motion and encodes the blockwithout applying an OBMC process. The decoder switches betweenapplication and non-application of an OBMC process by decoding theobmc_flag written in the stream (for example, a compressed sequence) anddecoding the block by switching between the application andnon-application of the OBMC process in accordance with the flag value.

Inter predictor 126 generates one rectangular prediction image for arectangular current block in the above example. However, inter predictor126 may generate a plurality of prediction images each having a shapedifferent from a rectangle for the rectangular current block, and maycombine the plurality of prediction images to generate the finalrectangular prediction image. The shape different from a rectangle maybe, for example, a triangle.

FIG. 37 is a conceptual diagram for illustrating generation of twotriangular prediction images.

Inter predictor 126 generates a triangular prediction image byperforming motion compensation of a first partition having a triangularshape in a current block by using a first MV of the first partition, togenerate a triangular prediction image. Likewise, inter predictor 126generates a triangular prediction image by performing motioncompensation of a second partition having a triangular shape in acurrent block by using a second MV of the second partition, to generatea triangular prediction image. Inter predictor 126 then generates aprediction image having the same rectangular shape as the rectangularshape of the current block by combining these prediction images.

It is to be noted that, although the first partition and the secondpartition are triangles in the example illustrated in FIG. 37, the firstpartition and the second partition may be trapezoids, or other shapesdifferent from each other. Furthermore, although the current blockincludes two partitions in the example illustrated in FIG. 37, thecurrent block may include three or more partitions.

In addition, the first partition and the second partition may overlapwith each other. In other words, the first partition and the secondpartition may include the same pixel region. In this case, a predictionimage for a current block may be generated using a prediction image inthe first partition and a prediction image in the second partition.

In addition, although an example in which a prediction image isgenerated for each of two partitions using inter prediction, aprediction image may be generated for at least one partition using intraprediction.

[Motion Compensation>BIO]

Next, a method for deriving a motion vector is described. First, a modefor deriving a motion vector based on a model assuming uniform linearmotion will be described. This mode is also referred to as abi-directional optical flow (BIO) mode.

FIG. 38 is a conceptual diagram for illustrating a model assuminguniform linear motion. In FIG. 38, (vx, vy) indicates a velocity vector,and τ0 and τ1 indicate temporal distances between a current picture (CurPic) and two reference pictures (Ref0, Ref1). (MVx0, MVy0) indicatemotion vectors corresponding to reference picture Ref0, and (MVx1, MVy1)indicate motion vectors corresponding to reference picture Ref1.

Here, under the assumption of uniform linear motion exhibited byvelocity vectors (v_(x), v_(y)), (MVx₀, MVy₀) and (MVx₁, MVy₁) arerepresented as (v_(x)τ₀, v_(y)τ₀) and (−v_(x)τ₁, −v_(y)τ₁),respectively, and the following optical flow equation (2) may beemployed.

[MATH. 3]

∂I ^((k)) /∂t+v _(x) ∂I ^((k)) /∂x+v _(y) ∂I ^((k)) /∂y=0.  (2)

Here, I(k) indicates a motion-compensated luma value of referencepicture k (k=0, 1). This optical flow equation shows that the sum of (i)the time derivative of the luma value, (ii) the product of thehorizontal velocity and the horizontal component of the spatial gradientof a reference image, and (iii) the product of the vertical velocity andthe vertical component of the spatial gradient of a reference image isequal to zero. A motion vector of each block obtained from, for example,a merge list may be corrected in units of a pixel, based on acombination of the optical flow equation and Hermite interpolation.

It is to be noted that a motion vector may be derived on the decoderside using a method other than deriving a motion vector based on a modelassuming uniform linear motion. For example, a motion vector may bederived in units of a sub-block based on motion vectors of neighboringblocks.

[Motion Compensation>LIC]

Next, an example of a mode in which a prediction image (prediction) isgenerated by using a local illumination compensation (LIC) process willbe described.

FIG. 39 is a conceptual diagram for illustrating one example of aprediction image generation method using a luminance correction processperformed by a LIC process.

First, an MV is derived from an encoded reference picture, and areference image corresponding to the current block is obtained.

Next, information indicating how the luma value changed between thereference picture and the current picture is extracted for the currentblock. This extraction is performed based on the luma pixel values forthe encoded left neighboring reference region (surrounding referenceregion) and the encoded upper neighboring reference region (surroundingreference region), and the luma pixel value at the correspondingposition in the reference picture specified by the derived MV. Aluminance correction parameter is calculated by using the informationindicating how the luma value changed.

The prediction image for the current block is generated by performing aluminance correction process in which the luminance correction parameteris applied to the reference image in the reference picture specified bythe MV.

It is to be noted that the shape of the surrounding reference regionillustrated in FIG. 39 is just one example; the surrounding referenceregion may have a different shape.

Moreover, although the process in which a prediction image is generatedfrom a single reference picture has been described here, cases in whicha prediction image is generated from a plurality of reference picturescan be described in the same manner. The prediction image may begenerated after performing a luminance correction process of thereference images obtained from the reference pictures in the same manneras described above.

One example of a method for determining whether to apply a LIC processis a method for using a lic_flag which is a signal indicating whether toapply the LIC process. As one specific example, the encoder determineswhether the current block belongs to a region having a luminance change.The encoder sets the lic_flag to a value of “1” when the block belongsto a region having a luminance change and applies a LIC process whenencoding, and sets the lic_flag to a value of “0” when the block doesnot belong to a region having a luminance change and encodes the currentblock without applying a LIC process. The decoder may decode thelic_flag written in the stream and decode the current block by switchingbetween application and non-application of a LIC process in accordancewith the flag value.

One example of a different method of determining whether to apply a LICprocess is a determining method in accordance with whether a LIC processwas applied to a surrounding block. In one specific example, when themerge mode is used on the current block, whether a LIC process wasapplied in the encoding of the surrounding encoded block selected uponderiving the MV in the merge mode process is determined. According tothe result, encoding is performed by switching between application andnon-application of a LIC process. It is to be noted that, also in thisexample, the same processes are applied in processes at the decoderside.

An embodiment of the luminance correction (LIC) process described withreference to FIG. 39 is described in detail below.

First, inter predictor 126 derives a motion vector for obtaining areference image corresponding to a current block to be encoded from areference picture which is an encoded picture.

Next, inter predictor 126 extracts information indicating how the lumavalue of the reference picture has been changed to the luma value of thecurrent picture, using the luma pixel value of an encoded surroundingreference region which neighbors to the left of or above the currentblock and the luma value in the corresponding position in the referencepicture specified by a motion vector, and calculates a luminancecorrection parameter. For example, it is assumed that the luma pixelvalue of a given pixel in the surrounding reference region in thecurrent picture is p0, and that the luma pixel value of the pixelcorresponding to the given pixel in the surrounding reference region inthe reference picture is p1. Inter predictor 126 calculates coefficientsA and B for optimizing A×p1+B=p0 as the luminance correction parameterfor a plurality of pixels in the surrounding reference region.

Next, inter predictor 126 performs a luminance correction process usingthe luminance correction parameter for the reference image in thereference picture specified by the motion vector, to generate aprediction image for the current block. For example, it is assumed thatthe luma pixel value in the reference image is p2, and that theluminance-corrected luma pixel value of the prediction image is p3.Inter predictor 126 generates the prediction image after being subjectedto the luminance correction process by calculating A×p2+B=p3 for each ofthe pixels in the reference image.

It is to be noted that the shape of the surrounding reference regionillustrated in FIG. 39 is one example; a different shape other than theshape of the surrounding reference region may be used. In addition, partof the surrounding reference region illustrated in FIG. 39 may be used.For example, a region having a determined number of pixels extractedfrom each of an upper neighboring pixel and a left neighboring pixel maybe used as a surrounding reference region. The determined number ofpixels may be predetermined.

In addition, the surrounding reference region is not limited to a regionwhich neighbors the current block, and may be a region which does notneighbor the current block. In the example illustrated in FIG. 39, thesurrounding reference region in the reference picture is a regionspecified by a motion vector in a current picture, from a surroundingreference region in the current picture. However, a region specified byanother motion vector is also possible. For example, the other motionvector may be a motion vector in a surrounding reference region in thecurrent picture.

Although operations performed by encoder 100 have been described here,it is to be noted that decoder 200 typically performs similaroperations.

It is to be noted that the LIC process may be applied not only to theluma but also to chroma. At this time, a correction parameter may bederived individually for each of Y, Cb, and Cr, or a common correctionparameter may be used for any of Y, Cb, and Cr.

In addition, the LIC process may be applied in units of a sub-block. Forexample, a correction parameter may be derived using a surroundingreference region in a current sub-block and a surrounding referenceregion in a reference sub-block in a reference picture specified by anMV of the current sub-block.

[Prediction Controller]

Inter predictor 128 selects one of an intra prediction signal (a signaloutput from intra predictor 124) and an inter prediction signal (asignal output from inter predictor 126), and outputs the selected signalto subtractor 104 and adder 116 as a prediction signal.

As illustrated in FIG. 1, in various kinds of encoder examples,prediction controller 128 may output a prediction parameter which isinput to entropy encoder 110. Entropy encoder 110 may generate anencoded bitstream (or a sequence), based on the prediction parameterwhich is input from prediction controller 128 and quantized coefficientswhich are input from quantizer 108. The prediction parameter may be usedin a decoder. The decoder may receive and decode the encoded bitstream,and perform the same processes as the prediction processes performed byintra predictor 124, inter predictor 126, and prediction controller 128.The prediction parameter may include (i) a selection prediction signal(for example, a motion vector, a prediction type, or a prediction modeused by intra predictor 124 or inter predictor 126), or (ii) an optionalindex, a flag, or a value which is based on a prediction processperformed in each of intra predictor 124, inter predictor 126, andprediction controller 128, or which indicates the prediction process.

[Mounting Example of Encoder]

FIG. 40 is a block diagram illustrating a mounting example of encoder100. Encoder 100 includes processor a1 and memory a2. For example, theplurality of constituent elements of encoder 100 illustrated in FIG. 1are mounted on processor a1 and memory a2 illustrated in FIG. 40.

Processor a1 is circuitry which performs information processing and isaccessible to memory a2. For example, processor a1 is dedicated orgeneral electronic circuitry which encodes a video. Processor a1 may bea processor such as a CPU. In addition, processor a1 may be an aggregateof a plurality of electronic circuits. In addition, for example,processor a1 may take the roles of two or more constituent elements outof the plurality of constituent elements of encoder 100 illustrated inFIG. 1, etc.

Memory a2 is dedicated or general memory for storing information that isused by processor a1 to encode a video. Memory a2 may be electroniccircuitry, and may be connected to processor a1. In addition, memory a2may be included in processor a1. In addition, memory a2 may be anaggregate of a plurality of electronic circuits. In addition, memory a2may be a magnetic disc, an optical disc, or the like, or may berepresented as a storage, a recording medium, or the like. In addition,memory a2 may be non-volatile memory, or volatile memory.

For example, memory a2 may store a video to be encoded or a bitstreamcorresponding to an encoded video. In addition, memory a2 may store aprogram for causing processor a1 to encode a video.

In addition, for example, memory a2 may take the roles of two or moreconstituent elements for storing information out of the plurality ofconstituent elements of encoder 100 illustrated in FIG. 1, etc. Forexample, memory a2 may take the roles of block memory 118 and framememory 122 illustrated in FIG. 1. More specifically, memory a2 may storea reconstructed block, a reconstructed picture, etc.

It is to be noted that, in encoder 100, all of the plurality ofconstituent elements indicated in FIG. 1, etc. may not be implemented,and all the processes described above may not be performed. Part of theconstituent elements indicated in FIG. 1, etc. may be included inanother device, or part of the processes described above may beperformed by another device.

[Decoder]

Next, a decoder capable of decoding an encoded signal (encodedbitstream) output, for example, from encoder 100 described above will bedescribed. FIG. 41 is a block diagram illustrating a functionalconfiguration of decoder 200 according to an embodiment. Decoder 200 isa video decoder which decodes a video in units of a block.

As illustrated in FIG. 41, decoder 200 includes entropy decoder 202,inverse quantizer 204, inverse transformer 206, adder 208, block memory210, loop filter 212, frame memory 214, intra predictor 216, interpredictor 218, and prediction controller 220.

Decoder 200 is implemented as, for example, a generic processor andmemory. In this case, when a software program stored in the memory isexecuted by the processor, the processor functions as entropy decoder202, inverse quantizer 204, inverse transformer 206, adder 208, loopfilter 212, intra predictor 216, inter predictor 218, and predictioncontroller 220. Alternatively, decoder 200 may be implemented as one ormore dedicated electronic circuits corresponding to entropy decoder 202,inverse quantizer 204, inverse transformer 206, adder 208, loop filter212, intra predictor 216, inter predictor 218, and prediction controller220.

Hereinafter, an overall flow of processes performed by decoder 200 isdescribed, and then each of constituent elements included in decoder 200will be described.

[Overall Flow of Decoding Process]

FIG. 42 is a flow chart illustrating one example of an overall decodingprocess performed by decoder 200.

First, entropy decoder 202 of decoder 200 identifies a splitting patternof a block having a fixed size (for example, 128×128 pixels) (StepSp_1). This splitting pattern is a splitting pattern selected by encoder100. Decoder 200 then performs processes of Step Sp_2 to Sp_6 for eachof a plurality of blocks of the splitting pattern.

In other words, entropy decoder 202 decodes (specifically,entropy-decodes) encoded quantized coefficients and a predictionparameter of a current block to be decoded (also referred to as acurrent block) (Step Sp_2).

Next, inverse quantizer 204 performs inverse quantization of theplurality of quantized coefficients and inverse transformer 206 performsinverse transform of the result, to restore a plurality of predictionresiduals (that is, a difference block) (Step Sp_3).

Next, the prediction processor including all or part of intra predictor216, inter predictor 218, and prediction controller 220 generates aprediction signal (also referred to as a prediction block) of thecurrent block (Step Sp_4).

Next, adder 208 adds the prediction block to the difference block togenerate a reconstructed image (also referred to as a decoded imageblock) of the current block (Step Sp_5).

When the reconstructed image is generated, loop filter 212 performsfiltering of the reconstructed image (Step Sp_6).

Decoder 200 then determines whether decoding of the entire picture hasbeen finished (Step Sp_7). When determining that the decoding has notyet been finished (No in Step Sp_7), decoder 200 repeatedly executes theprocesses starting with Step Sp_1.

As illustrated, the processes of Steps Sp_1 to Sp_7 are performedsequentially by decoder 200. Alternatively, two or more of the processesmay be performed in parallel, the processing order of the two or more ofthe processes may be modified, etc.

[Entropy Decoder]

Entropy decoder 202 entropy decodes an encoded bitstream. Morespecifically, for example, entropy decoder 202 arithmetic decodes anencoded bitstream into a binary signal. Entropy decoder 202 thendebinarizes the binary signal. With this, entropy decoder 202 outputsquantized coefficients of each block to inverse quantizer 204. Entropydecoder 202 may output a prediction parameter included in an encodedbitstream (see FIG. 1) to intra predictor 216, inter predictor 218, andprediction controller 220. Intra predictor 216, inter predictor 218, andprediction controller 220 in an embodiment are capable of executing thesame prediction processes as those performed by intra predictor 124,inter predictor 126, and prediction controller 128 at the encoder side.

[Inverse Quantizer]

Inverse quantizer 204 inverse quantizes quantized coefficients of ablock to be decoded (hereinafter referred to as a current block) whichare inputs from entropy decoder 202. More specifically, inversequantizer 204 inverse quantizes quantized coefficients of the currentblock, based on quantization parameters corresponding to the quantizedcoefficients. Inverse quantizer 204 then outputs the inverse quantizedtransform coefficients of the current block to inverse transformer 206.

[Inverse Transformer]

Inverse transformer 206 restores prediction errors by inversetransforming the transform coefficients which are inputs from inversequantizer 204.

For example, when information parsed from an encoded bitstream indicatesthat EMT or AMT is to be applied (for example, when an AMT flag istrue), inverse transformer 206 inverse transforms the transformcoefficients of the current block based on information indicating theparsed transform type.

Moreover, for example, when information parsed from an encoded bitstreamindicates that NSST is to be applied, inverse transformer 206 applies asecondary inverse transform to the transform coefficients.

[Adder]

Adder 208 reconstructs the current block by adding prediction errorswhich are inputs from inverse transformer 206 and prediction sampleswhich are inputs from prediction controller 220. Adder 208 then outputsthe reconstructed block to block memory 210 and loop filter 212.

[Block Memory]

Block memory 210 is storage for storing blocks in a picture to bedecoded (hereinafter referred to as a current picture) and to bereferred to in intra prediction. More specifically, block memory 210stores reconstructed blocks output from adder 208.

[Loop Filter]

Loop filter 212 applies a loop filter to blocks reconstructed by adder208, and outputs the filtered reconstructed blocks to frame memory 214,display device, etc.

When information indicating ON or OFF of an ALF parsed from an encodedbitstream indicates that an ALF is ON, one filter from among a pluralityof filters is selected based on direction and activity of localgradients, and the selected filter is applied to the reconstructedblock.

[Frame Memory]

Frame memory 214 is, for example, storage for storing reference picturesfor use in inter prediction, and is also referred to as a frame buffer.More specifically, frame memory 214 stores a reconstructed blockfiltered by loop filter 212.

[Prediction Processor (Intra Predictor, Inter Predictor, PredictionController)]

FIG. 43 is a flow chart illustrating one example of a process performedby a prediction processor of decoder 200. It is to be noted that theprediction processor includes all or part of the following constituentelements: intra predictor 216; inter predictor 218; and predictioncontroller 220.

The prediction processor generates a prediction image of a current block(Step Sq_1). This prediction image is also referred to as a predictionsignal or a prediction block. It is to be noted that the predictionsignal is, for example, an intra prediction signal or an interprediction signal. Specifically, the prediction processor generates theprediction image of the current block using a reconstructed image whichhas been already obtained through generation of a prediction block,generation of a difference block, generation of a coefficient block,restoring of a difference block, and generation of a decoded imageblock.

The reconstructed image may be, for example, an image in a referencepicture, or an image of a decoded block in a current picture which isthe picture including the current block. The decoded block in thecurrent picture is, for example, a neighboring block of the currentblock.

FIG. 44 is a flow chart illustrating another example of a processperformed by the prediction processor of decoder 200.

The prediction processor determines either a method or a mode forgenerating a prediction image (Step Sr_1). For example, the method ormode may be determined based on, for example, a prediction parameter,etc.

When determining a first method as a mode for generating a predictionimage, the prediction processor generates a prediction image accordingto the first method (Step Sr_2 a). When determining a second method as amode for generating a prediction image, the prediction processorgenerates a prediction image according to the second method (Step Sr_2b). When determining a third method as a mode for generating aprediction image, the prediction processor generates a prediction imageaccording to the third method (Step Sr_2 c).

The first method, the second method, and the third method may bemutually different methods for generating a prediction image. Each ofthe first to third methods may be an inter prediction method, an intraprediction method, or another prediction method. The above-describedreconstructed image may be used in these prediction methods.

[Intra Predictor]

Intra predictor 216 generates a prediction signal (intra predictionsignal) by performing intra prediction by referring to a block or blocksin the current picture stored in block memory 210, based on the intraprediction mode parsed from the encoded bitstream. More specifically,intra predictor 216 generates an intra prediction signal by performingintra prediction by referring to samples (for example, luma and/orchroma values) of a block or blocks neighboring the current block, andthen outputs the intra prediction signal to prediction controller 220.

It is to be noted that when an intra prediction mode in which a lumablock is referred to in intra prediction of a chroma block is selected,intra predictor 216 may predict the chroma component of the currentblock based on the luma component of the current block.

Moreover, when information parsed from an encoded bitstream indicatesthat PDPC is to be applied, intra predictor 216 corrects intra-predictedpixel values based on horizontal/vertical reference pixel gradients.

[Inter Predictor]

Inter predictor 218 predicts the current block by referring to areference picture stored in frame memory 214. Inter prediction isperformed in units of a current block or a sub-block (for example, a 4×4block) in the current block. For example, inter predictor 218 generatesan inter prediction signal of the current block or the sub-block byperforming motion compensation by using motion information (for example,a motion vector) parsed from an encoded bitstream (for example, aprediction parameter output from entropy decoder 202), and outputs theinter prediction signal to prediction controller 220.

It is to be noted that when the information parsed from the encodedbitstream indicates that the OBMC mode is to be applied, inter predictor218 generates the inter prediction signal using motion information of aneighboring block in addition to motion information of the current blockobtained from motion estimation.

Moreover, when the information parsed from the encoded bitstreamindicates that the FRUC mode is to be applied, inter predictor 218derives motion information by performing motion estimation in accordancewith the pattern matching method (bilateral matching or templatematching) parsed from the encoded bitstream. Inter predictor 218 thenperforms motion compensation (prediction) using the derived motioninformation.

Moreover, when the BIO mode is to be applied, inter predictor 218derives a motion vector based on a model assuming uniform linear motion.Moreover, when the information parsed from the encoded bitstreamindicates that the affine motion compensation prediction mode is to beapplied, inter predictor 218 derives a motion vector of each sub-blockbased on motion vectors of neighboring blocks.

[MV Derivation>Normal Inter Mode]

When information parsed from an encoded bitstream indicates that thenormal inter mode is to be applied, inter predictor 218 derives an MVbased on the information parsed from the encoded bitstream and performsmotion compensation (prediction) using the MV.

FIG. 45 is a flow chart illustrating an example of inter prediction innormal inter mode in decoder 200.

Inter predictor 218 of decoder 200 performs motion compensation for eachblock. Inter predictor 218 obtains a plurality of MV candidates for acurrent block based on information such as MVs of a plurality of decodedblocks temporally or spatially surrounding the current block (StepSs_1). In other words, inter predictor 218 generates an MV candidatelist.

Next, inter predictor 218 extracts N (an integer of 2 or larger) MVcandidates from the plurality of MV candidates obtained in Step Ss_1, asmotion vector predictor candidates (also referred to as MV predictorcandidates) according to a determined priority order (Step Ss_2). It isto be noted that the priority order may be determined in advance foreach of the N MV predictor candidates.

Next, inter predictor 218 decodes motion vector predictor selectioninformation from an input stream (that is, an encoded bitstream), andselects, one MV predictor candidate from the N MV predictor candidatesusing the decoded motion vector predictor selection information, as amotion vector (also referred to as an MV predictor) of the current block(Step Ss_3).

Next, inter predictor 218 decodes an MV difference from the inputstream, and derives an MV for a current block by adding a differencevalue which is the decoded MV difference and a selected motion vectorpredictor (Step Ss_4).

Lastly, inter predictor 218 generates a prediction image for the currentblock by performing motion compensation of the current block using thederived MV and the decoded reference picture (Step Ss_5).

[Prediction Controller]

Prediction controller 220 selects either the intra prediction signal orthe inter prediction signal, and outputs the selected prediction signalto adder 208. As a whole, the configurations, functions, and processesof prediction controller 220, intra predictor 216, and inter predictor218 at the decoder side may correspond to the configurations, functions,and processes of prediction controller 128, intra predictor 124, andinter predictor 126 at the encoder side.

[Mounting Example of Decoder]

FIG. 46 is a block diagram illustrating a mounting example of decoder200. Decoder 200 includes processor b1 and memory b2. For example, theplurality of constituent elements of decoder 200 illustrated in FIG. 41are mounted on processor b1 and memory b2 illustrated in FIG. 46.

Processor b1 is circuitry which performs information processing and isaccessible to memory b2. For example, processor b1 is dedicated orgeneral electronic circuitry which decodes a video (that is, an encodedbitstream). Processor b1 may be a processor such as a CPU. In addition,processor b1 may be an aggregate of a plurality of electronic circuits.In addition, for example, processor b1 may take the roles of two or moreconstituent elements out of the plurality of constituent elements ofdecoder 200 illustrated in FIG. 41, etc.

Memory b2 is dedicated or general memory for storing information that isused by processor b1 to decode an encoded bitstream. Memory b2 may beelectronic circuitry, and may be connected to processor b1. In addition,memory b2 may be included in processor b1. In addition, memory b2 may bean aggregate of a plurality of electronic circuits. In addition, memoryb2 may be a magnetic disc, an optical disc, or the like, or may berepresented as a storage, a recording medium, or the like. In addition,memory b2 may be a non-volatile memory, or a volatile memory.

For example, memory b2 may store a video or a bitstream. In addition,memory b2 may store a program for causing processor b1 to decode anencoded bitstream.

In addition, for example, memory b2 may take the roles of two or moreconstituent elements for storing information out of the plurality ofconstituent elements of decoder 200 illustrated in FIG. 41, etc.Specifically, memory b2 may take the roles of block memory 210 and framememory 214 illustrated in FIG. 41. More specifically, memory b2 maystore a reconstructed block, a reconstructed picture, etc.

It is to be noted that, in decoder 200, all of the plurality ofconstituent elements illustrated in FIG. 41, etc. may not beimplemented, and all the processes described above may not be performed.Part of the constituent elements indicated in FIG. 41, etc. may beincluded in another device, or part of the processes described above maybe performed by another device.

Definitions of Terms

The respective terms may be defined as indicated below as examples.

A picture is an array of luma samples in monochrome format or an arrayof luma samples and two corresponding arrays of chroma samples in 4:2:0,4:2:2, and 4:4:4 color format. A picture may be either a frame or afield.

A frame is the composition of a top field and a bottom field, wheresample rows 0, 2, 4, . . . originate from the top field and sample rows1, 3, 5, . . . originate from the bottom field.

A slice is an integer number of coding tree units contained in oneindependent slice segment and all subsequent dependent slice segments(if any) that precede the next independent slice segment (if any) withinthe same access unit.

A tile is a rectangular region of coding tree blocks within a particulartile column and a particular tile row in a picture. A tile may be arectangular region of the frame that is intended to be able to bedecoded and encoded independently, although loop-filtering across tileedges may still be applied.

A block is an M×N (M-column by N-row) array of samples, or an M×N arrayof transform coefficients. A block may be a square or rectangular regionof pixels including one Luma and two Chroma matrices.

A coding tree unit (CTU) may be a coding tree block of luma samples of apicture that has three sample arrays, or two corresponding coding treeblocks of chroma samples. Alternatively, a CTU may be a coding treeblock of samples of one of a monochrome picture and a picture that iscoded using three separate color planes and syntax structures used tocode the samples.

A super block may be a square block of 64×64 pixels that consists ofeither 1 or 2 mode info blocks or is recursively partitioned into four32×32 blocks, which themselves can be further partitioned.

[Description of Outline of a BDOF (BIO) Process]

The outline of the BDOF (BIO) process is described again with referenceto FIGS. 38, 47, and 48.

FIG. 47 is a flow chart indicating one example of inter predictionaccording to BIO. In addition, FIG. 48 is a diagram illustrating oneexample of a functional configuration of inter predictor 126 whichperforms inter prediction according to BIO.

As illustrated in FIG. 48, inter predictor 126 includes, for example,memory 126 a, interpolated image deriver 126 b, gradient image deriver126 c, optical flow deriver 126 d, correction value deriver 126 e, andprediction image corrector 126 f. It is to be noted that memory 126 amay be frame memory 122.

Inter predictor 126 derives two motion vectors (M0, M1) using tworeference pictures (Ref0, Ref1) different from a picture (Cur Pic)including a current block. Inter predictor 126 then derives a predictionimage for the current block using the two motion vectors (M0, M1) (StepSy_1). It is to be noted that motion vector M0 is a motion vector (MVx0,MVy0) corresponding to reference picture Ref0, and motion vector M1 is amotion vector (MVx1, MVy1) corresponding to reference picture Ref1.

Next, interpolated image deriver 126 b derives interpolated image I⁰ forthe current block using motion vector M0 and reference picture L0 withreference to memory 126 a. In addition, interpolated image deriver 126 bderives interpolated image I¹ for the current block using motion vectorM1 and reference picture L1 with reference to memory 126 a (Step Sy_2).Here, interpolated image I⁰ is an image included in reference pictureRef0 and to be derived for the current block, and interpolated image I¹is an image included in reference picture Ref1 and to be derived for thecurrent block. Each of interpolated image I⁰ and interpolated image I¹may be the same in size as the current block. Alternatively, each ofinterpolated image I⁰ and interpolated image I¹ may be an image largerthan the current block in order to appropriately derive a gradient imageto be described later. Furthermore, interpolated image I⁰ andinterpolated image I¹ may include the motion vectors (M0, M1), thereference pictures (L0, L1), and a prediction image derived by applyinga motion compensation filter.

In addition, gradient image deriver 126 c derives gradient images (Ix⁰,Ix¹, Iy⁰, Iy¹) of the current block from interpolated image I⁰ andinterpolated image I¹ (Step Sy_3). It is to be noted that the gradientimages in the horizontal direction are (Ix⁰, Ix¹), and the gradientimages in the vertical direction are (Iy⁰, Iy¹). Gradient image deriver126 c may derive the gradient images by, for example, applying agradient filter to the interpolated images. Gradient images may be theones each of which indicates the amount of spatial change in pixel valuealong the horizontal direction or the vertical direction.

Next, optical flow deriver 126 d derives, for each sub-block of thecurrent block, an optical flow (vx, vy) which is the above-describedvelocity vector, using the interpolated images (I⁰, I¹) and the gradientimages (Ix⁰, Ix¹, Iy⁰, Iy¹) (Step Sy_4). An optical flow is acoefficient for correcting the amount of spatial pixel movement, and maybe referred to as a local motion estimated value, a corrected motionvector, or a corrected weighting vector. As one example, a sub-block maybe 4×4 pixel sub-CU. It is to be noted that the optical flow may bederived not in units of a sub-block, but in other units, for example, inunits of a pixel.

Next, inter predictor 126 corrects a prediction image for the currentblock using the optical flow (vx, vy). For example, correction valuederiver 126 e derives a correction value for the value of a pixelincluded in the current block using the optical flow (vx, vy) (StepSy_5). Prediction image corrector 126 f may then correct the predictionimage for the current block using the correction value (Step Sy_6). Itis to be noted that the correction value may be derived in units of apixel, or may be derived in units of a plurality of pixels or in unitsof a sub-block.

It is to be noted that the BIO process flow is not limited to theprocess disclosed in FIG. 47. Only part of the processes disclosed inFIG. 47 may be performed, or a different process may be added or used asa replacement, or the processes may be executed in a differentprocessing order.

For example, BDOF (BIO) may be defined as a process of generating acorrected prediction image using a gradient of a reference block.Alternatively, BDOF may be defined as a process of generating aprediction image using gradients of two reference blocks. Alternatively,BDOF may be defined as a process of generating a prediction image usinga gradient in a mode different from an affine mode. Alternatively, BDOFmay be defined as an optical flow process in a mode different from anaffine mode. Here, the gradient means a spatial gradient of a pixelvalue.

[First Specific Example of BIO]

Next, a first specific example of a decoding process based on BIO isdescribed with reference to FIGS. 49, 50, and 51. For example, decoder200 calculates a BIO parameter from two reference blocks which have beenmotion compensated, and decodes a current block using the BIO parametercalculated. A BIO parameter is a parameter corresponding to the opticalflow described above. The BIO parameter is also referred to as a localmotion estimated value, a corrected motion vector, a corrected MV value,a corrected weighted motion vector, or a BIO correction value.

FIG. 49 is a flow chart indicating the first specific example of thedecoding process based on BIO. FIG. 50 is a conceptual diagramillustrating an example of calculating horizontal gradient values whichare gradient values in a horizontal direction. FIG. 51 is a conceptualdiagram illustrating an example of calculating vertical gradient valueswhich are gradient values in a vertical direction.

First, decoder 200 calculates a first sum for the current block, usingthe horizontal gradient value of a first reference block and thehorizontal gradient value of a second reference block (S1001). Thecurrent block may be a sub-block of a current coding unit (current CU)as illustrated in FIGS. 50 and 51.

The first reference block is a block which is to be referred to indecoding of the current block and is defined in reference picture L0 bythe current block or a first motion vector of the current CU. The secondreference block is a block which is to be referred to in decoding of thecurrent block and is defined in reference picture L1 by the currentblock or a second motion vector of the current CU.

Basically, reference picture L0 and reference picture L1 are twodifferent reference pictures, and the first reference block and thesecond reference block are two different reference blocks. In addition,here, the first reference block and the second reference block used herehave been adjusted respectively at a sub-pixel accuracy using a motioncompensation filter, and have the same size as the size of the currentblock.

When the current block is a sub-block in a current coding unit, each ofthe first reference block and the second reference block may be asub-block of the reference block in the current coding unit.

In other words, a plurality of pixel values in reference picture L0 inFIGS. 50 and 51 may be a plurality of pixel values in a block defined asa reference block in the current coding unit, for reference picture L0.Likewise, a plurality of pixel values in reference picture L1 in FIGS.50 and 51 may be a plurality of pixel values in a block defined as areference block in the current coding unit, for reference picture L1.

Decoder 200 calculates a first sum using a horizontal gradient value ofthe above-mentioned first reference block and a horizontal gradientvalue of the above-mentioned second reference block. Decoder 200 maycalculate a first sum using not only the horizontal gradient value ofthe first reference block and the horizontal gradient value of thesecond reference block, but also a horizontal gradient value of aneighboring area that neighbors the first reference block and ahorizontal gradient value of a neighboring area that neighbors thesecond reference block. Expressions (3.1) and (3.2) indicated belowindicate an example of a method for a calculation process of a secondsum.

[Math. 4]

G _(x) =I _(x) ⁰ +I _(x) ¹  (3.1)

[Math. 5]

sG _(x)=Σ_([i,j]∈Ω)sign(G _(x)[i,j])×G _(x)[i,j]  (3.2)

Here, × denotes multiplication, and + denotes addition. In addition,sign denotes a plus or minus sign. Specifically, sign denotes a as aplus value, and −1 as a minus value. Specifically, sign denotes, forexample, the following.

[Math.  6] $\begin{matrix}{{{sign}(x)} = \{ \begin{matrix}1 & {{{if}\mspace{20mu} x} \geq 0} \\{- 1} & {{{if}\mspace{20mu} x} < 0}\end{matrix} } & (a)\end{matrix}$

As a result, sign (G_(x) [i, j])×G_(x) [i, j] becomes G_(x) [i, j]without sign change when G_(x) [i, j] is a plus value, and becomes−G_(x) [i, j] when G_(x) [i, j] is a minus value. Thus, the calculationis equivalent to derivation of an absolute value (abs) of G_(x) [i, j]).

In Expression (3.1), I_(x) ⁰ denotes a horizontal gradient value in thefirst reference block in reference picture L0, and I_(x) ¹ denotes ahorizontal gradient value in the second reference block in referencepicture L1.

An example of a horizontal gradient filter for obtaining horizontalgradient values is a three-tap filter having a filter coefficient set of[−1, 0, 1]. The horizontal gradient value in the first reference blockis calculated by applying a horizontal gradient filter to a plurality ofreference pixels in the first reference block. The horizontal gradientvalue in the second reference block is calculated by applying ahorizontal gradient filter to a plurality of reference pixels in thesecond reference block.

In the example illustrated in FIG. 50, horizontal gradient value I_(x) ⁰of the pixel located at position [3, 2] in the first reference block iscalculated as a matrix product [−1, 0, 1]^(T)[2, 3, 5], and theresulting value is 3. Horizontal gradient value I_(x) ¹ of the pixellocated at position [3, 2] in the second reference block is calculatedas a matrix product [−1, 0, 1]^(T)[5, 3, 2], and the resulting value is−3. It is to be noted that [a, b, c] denotes a matrix having three rowsand one column.

In Expression (3.2), sG_(x) denotes the first sum, and is calculated asa sum of absolute values of G_(x) over a window denoted as Ω. The sizeof window Ω may be the same as the size of a current block.Alternatively, the size of window Ω may be larger than the size of acurrent block. In the latter case, the value of G_(x) at a positionneighboring the current block is included in a process of calculating afirst sum.

As in the case of the first sum which is the sum of the horizontalgradient values, decoder 200 calculates a second sum for the currentblock, using a vertical gradient value of a first reference block and avertical gradient value of a second reference block (S1002). Expressions(3.3) and (3.4) indicated below indicate an example of a method for acalculation process of a second sum.

[Math. 7]

G _(y) =I _(y) ⁰ +I _(y) ¹  (3.3)

[Math. 8]

sG _(y)=Σ_([i,j]∈Ω)sign(G _(y)[i,j])×G _(y)[i,j]  (3.4)

In Expression (3.3), I_(y) ⁰ denotes a vertical gradient value in thefirst reference block in reference picture L0, and I_(y) ¹ denotes avertical gradient value in the second reference block in referencepicture L1.

An example of a vertical gradient filter for obtaining vertical gradientvalues is a three-tap filter having a filter coefficient set of [−1, 0,1]. The vertical gradient value in the first reference block iscalculated by applying a vertical gradient filter to a plurality ofreference pixels in the first reference block. The vertical gradientvalue in the second reference block is calculated by applying a verticalgradient filter to a plurality of reference pixels in the secondreference block.

In the example illustrated in FIG. 51, vertical gradient value I_(y) ⁰of the pixel located at position [3, 2] in the first reference block iscalculated as a matrix product [−1, 0, 1]^(T)[2, 3, 5], and theresulting value is 3. Vertical gradient value I_(y) ¹ of the pixellocated at position [3, 2] in the second reference block is calculatedas a matrix product [−1, 0, 1]^(T)[5, 3, 2], and the resulting value is−3.

In Expression (3.4), sG_(y) denotes the second sum, and is calculated asa sum of absolute values of G_(y) over the window denoted as Ω. When thesize of window Ω is larger than the value of the current block, valueG_(y) at a position neighboring the current block is included in aprocess of calculating a second sum.

Next, decoder 200 judges whether the first sum is larger than the secondsum (S1003). When judging that the first sum is larger than the secondsum (Yes in S1003), decoder 200 determines a BIO parameter for thecurrent block without using any vertical gradient value (S1004).Expressions (3.5) to (3.9) indicate an example of a computation processfor determining the BIO parameter in this case. According to theseexpressions, the BIO parameter denoted as u is calculated usinghorizontal gradient values.

[Math. 9]

sG _(x) dI=Σ _([i,j]∈Ω)sign(G _(x)[i,j])×(I ⁰ _(i,j) −I ¹ _(i,j))  (3.5)

[Math. 10]

denominator=sG _(x)  (3.6)

[Math. 11]

numerator=sG _(x) dI  (3.7)

[Math. 12]

shift=Bits(denominator)−6  (3.8)

[Math. 13]

u=Clip(((numerator>>(shift−12))×BIOShift[demoninator>>shift])>>27)  (3.9)

Here, − denotes subtraction, and >> denotes shift computation. Forexample, a>>b means that a is shifted to the right by b bits. Inaddition, Bits, BIOShift, and Clip respectively indicate the following.It is to be noted that, in the description below, ceil and floor denotedecimal round up and decimal round down, respectively.

$\begin{matrix}\begin{matrix}{{{Bits}\mspace{11mu}(x)} = \lceil {\log_{\; 2}x} \rceil} \\{{{{BIOShift}\;\lbrack i\rbrack} = \lfloor {( {( {1 ⪡ 15} ) + \lfloor {i/2} \rfloor} )/i} \rfloor};{i \in \lbrack {1,63} \rbrack}} \\{{{Clip}\mspace{11mu}(x)} = \{ \begin{matrix}256 & {{{if}\mspace{20mu} x} > 256} \\x & {{{if} - 256} \leq x \leq 256} \\{- 256} & {{{if}{\mspace{14mu}\;}x} < {- 256}}\end{matrix} } \\{\lceil x \rceil = {{ceil}(x)}} \\{\lfloor x \rfloor = {{floor}(x)}}\end{matrix} & \lbrack {{Math}.\mspace{14mu} 14} \rbrack\end{matrix}$

According to Expression (3.5), sG_(x)dI is calculated as a sum ofproducts of differences between I⁰ _(i, j) and I¹ _(i, j) and sign(G_(x) [i, j]) over window Ω. Here, I⁰ _(i, j) denotes the pixel valueat position [i, j] in the first reference block in reference picture L0,and I¹ _(i, j) denotes the pixel value at position [i, j] in the secondreference block in reference picture L1. I⁰ _(i, j) and I¹ _(i, j) maybe simply represented as I⁰ and I¹. BIO parameter u is calculated usingsG_(x)dI and sG_(x) according to Expressions (3.6) to (3.9).

When judging that the first sum is not larger than the second sum (No inS1003), decoder 200 determines BIO parameter u for the current blockwithout using any horizontal gradient value (S1005). Expressions (3.10)to (3.14) indicate an example of a computation process for determiningBIO parameter u in this case. Expressions (3.10) to (3.14) are basicallythe same as Expressions (3.5) to (3.9) except that BIO parameter u iscalculated using the vertical gradient values in Expression (3.10) to(3.14).

[Math. 15]

sG _(y) dI=Σ _([i,j]∈Ω)sign(G _(y)[i,j])×(I ⁰ _(i,j) −I ¹_(i,j))  (3.10)

[Math. 16]

denominator=sG _(y)  (3.11)

[Math. 17]

numerator=sG _(y) dI  (3.12)

[Math. 18]

shift=Bits(denominator)−6  (3.13)

[Math. 19]

u=Clip(((numerator>>(shift−12))×BIOShift[demoninator>>shift])>>27)  (3.14)

According to Expression (3.10), sG_(y)dI is calculated as a sum ofproducts of differences between I⁰ _(i, j) and I¹ _(i, j) and sign(G_(y) [i, j]) over window Ω. BIO parameter u is calculated usingsG_(y)dI and sG_(y) according to Expressions (3.11) to (3.14).

Decoder 200 then decodes the current block using BIO parameter u(S1006). Specifically, decoder 200 generates a prediction sample usingBIO parameter u, and decodes the current block using the predictionsample. Expressions (3.15) and (3.16) indicate an example of acomputation process for generating a prediction sample.

[Math. 20]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹))>>1  (3.15)

[Math. 21]

prediction sample=(I ⁰ +I ¹ +u×(I _(y) ⁰ −I _(y) ¹))>>1  (3.16)

When it is judged that the first sum is larger than the second sum (Yesin S1003). Expression (3.15) is used. When it is judged that the firstsum is not larger than the second sum (No in S1003), Expression (3.16)is used.

Decoder 200 may repeat the processes (S1001 to S1006) for all thesub-blocks in each of current CUs.

Decoder 200 is capable of increasing the accuracy of the predictionsample in the current block using BIO. Decoder 200 is further capable ofreducing increase in the amount of computation because decoder 200 usesonly one of the horizontal gradient values and the vertical gradientvalues when calculating a BIO parameter.

The above expressions are examples. Expressions for calculating a BIOparameter are not limited to the above expressions. For example, theplus or minus sign included in each expression may be changed, or anexpression equivalent to any of the above expressions may be used.Specifically, as an expression corresponding to Expressions (3.1) and(3.2) described above, following Expression (4.1) may be used.

[Math. 22]

sG _(x)=Σ_([i,j]∈Ω)abs(I _(x) ¹ +I _(x) ⁰)  (4.1)

In addition, for example, as an expression corresponding to Expression(3.5) described above, following Expression (4.2) may be used.

[Math. 23]

sG _(x) dI=Σ _([i,j]∈Ω)(−sign(I _(x) ¹ +I _(x) ⁰)×(I ⁰ −I ¹))  (4.2)

For example, as an expression corresponding to Expression (3.15)described above, following Expression (4.3) may be used.

[Math. 24]

prediction sample=(I ¹ +I ⁰ −u×(I _(x) ¹ −I _(x) ⁰))>>1  (4.3)

Expressions (3.6) to (3.9) substantially indicate division, and thus maybe represented as Expression (4.4).

[Math.  25] $\begin{matrix}{u = \frac{{sG}_{x}{dI}}{{sG}_{x}}} & (4.4)\end{matrix}$

Expressions (4.1) to (4.4) are substantially the same as Expressions(3.1), (3.2), (3.5) to (3.9), and (3.15) described above.

Likewise, specifically, as an expression corresponding to Expressions(3.3) and (3.4) described above, following Expression (4.5) may be used.

[Math. 26]

sG _(y)=Σ_([i,j]∈Ω)abs(I _(y) ¹ +I _(y) ⁰)  (4.5)

For example, as an expression corresponding to Expression (3.10)described above, following Expression (4.6) may be used.

[Math. 27]

sG _(y) dI=Σ _([i,j]∈Ω)(−sign(I _(y) ¹ +I _(y) ⁰)×(I ⁰ −I ¹))  (4.6)

For example, as an expression corresponding to Expression (3.16)described above, following Expression (4.7) may be used.

[Math. 28]

prediction sample=(I ¹ +I ⁰ −u×(I _(y) ¹ −I _(y) ⁰))>>1  (4.7)

Expressions (3.11) to (3.14) substantially indicate division, and thusmay be represented as Expression (4.8).

[Math.  29] $\begin{matrix}{u = \frac{{sG}_{y}{dI}}{{sG}_{y}}} & (4.8)\end{matrix}$

Expressions (4.5) to (4.8) are substantially the same as Expressions(3.3), (3.4), (3.10) to (3.14) and (3.16) described above.

In the above flow, the horizontal gradient value or the verticalgradient value is used based on the comparison between the first sum andthe second sum. However, decoding process flows are not limited to theflow described above. Whether to use a horizontal gradient value or avertical gradient value may be determined in advance by another codingparameter or the like. A BIO parameter may be derived using horizontalgradient values and a BIO parameter may be derived using verticalgradient values, without comparing a first sum and a second sum.Alternatively, only one of the first sum and the second sum may becalculated.

Even without comparing the first sum and the second sum, decoder 200 iscapable of reducing substantial multiplication which requires a largeamount of computation in the computations performed for the respectivepixel positions, and deriving a plurality of parameters for generatingthe prediction image with a small amount of computation. Specifically,although the plus or minus signs in Expressions (3.2), (3.4), (3.5),(3.10), (4.1), (4.2), (4.5), (4.6), etc. are changed, no substantialmultiplication is used. Accordingly, the number of times of substantialmultiplication in BIO processing can be reduced significantly.

In other words, decoder 200 is capable of calculating sG_(x), sG_(x)dI,sG_(y), and sG_(y)dI with a small amount of computation. Accordingly,decoder 200 is capable of reducing the processing amount in decoding.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, or a BIO parameter maybe replaced with one or more of expressions in the other specificexamples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

[Second Specific Example of BIO]

Next, a second specific example of a decoding process based on BIO isdescribed. For example, as in the first specific example, decoder 200calculates a BIO parameter from two reference blocks which have beenmotion compensated, and decodes a current block using the BIO parametercalculated.

In this specific example, a prediction sample for decoding a currentblock is generated according to Expressions (5.1) to (5.8) indicatedbelow.

[Math.  30] $\begin{matrix}{s_{1} = {{\Sigma_{{\lbrack{i,j}\rbrack} \in \Omega}( {{I_{x}}^{1} + {I_{x}}^{0}} )} \times ( {{I_{x}}^{1} + {I_{x}}^{0}} )}} & \; & {\mspace{169mu}(5.1)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 31} \rbrack$$\begin{matrix}{s_{2} = {{\Sigma_{{\lbrack{i,j}\rbrack} \in \Omega}( {{I_{y}}^{1} + {I_{y}}^{0}} )} \times ( {{I_{y}}^{1} + {I_{y}}^{0}} )}} & \; & {\mspace{166mu}(5.2)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 32} \rbrack$$\begin{matrix}{s_{3} = {\Sigma_{{\lbrack{i,j}\rbrack} \in \Omega}( {{- ( {{I_{x}}^{1} + {I_{x}}^{0}} )} \times ( {I^{0} - I^{1}} )} )}} & \; & {\mspace{149mu}(5.3)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 33} \rbrack$$\begin{matrix}{s_{4} = {\Sigma_{{\lbrack{i,j}\rbrack} \in \Omega}( {{- ( {{I_{y}}^{1} + {I_{y}}^{0}} )} \times ( {I^{0} - I^{1}} )} )}} & \; & {\mspace{149mu}(5.4)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 34} \rbrack$$\begin{matrix}{v_{x} = \frac{s_{3}}{s_{1}}} & \; & {\mspace{461mu}(5.5)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 35} \rbrack$$\begin{matrix}{v_{y} = \frac{s_{4}}{s_{2}}} & \; & {\mspace{461mu}(5.6)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 36} \rbrack$$\begin{matrix}{{offset} = {\frac{v_{x} \times ( {{I_{x}}^{0} + {I_{x}}^{1}} )}{2} + \frac{v_{y} \times ( {{I_{y}}^{0} + {I_{y}}^{1}} )}{2}}} & \; & {\mspace{95mu}(5.7)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 37} \rbrack$$\begin{matrix}{{{prediction}\mspace{14mu}{sample}} = \frac{I^{0} + I^{1} + {offset}}{2}} & \; & {\mspace{166mu}(5.8)}\end{matrix}$

S₁ in Expression (5.1) in this specific example corresponds to sG_(x) inExpression (3.2) in the first specific example. In addition, S₂ inExpression (5.2) in this specific example corresponds to sG_(y) inExpression (3.4) in the first specific example. In addition, S₃ inExpression (5.3) in this specific example corresponds to sG_(x)dI inExpression (3.5) in the first specific example. In addition, S₄ inExpression (5.4) in this specific example corresponds to sG_(y)dI inExpression (3.10) in the specific example.

Furthermore, v, and v, in Expressions (5.5) to (5.7) in this specificexample each correspond to a BIO parameter and correspond to u inExpressions (3.9) and (3.14) in the first specific example.

In the first specific example, no change is made to a plus or minus signand no substantial multiplication is performed in the calculation ofsG_(x), sG_(y), sG_(x)dI, and sG_(y)dI. In the specific example,substantial multiplication is performed in the calculation of S₁, S₂,S₃, and S₄. In this way, although the amount of computation increases, aprediction sample is generated with a higher accuracy. On the otherhand, the amount of computation is reduced in the first specificexample.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, or a BIO parameter maybe replaced with one or more of expressions in the other specificexamples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

[Third Specific Example of BIO]

Next, a third specific example of a decoding process based on BIO isdescribed with reference to FIG. 52. For example, as in the firstspecific example, decoder 200 calculates at least one BIO parameter fromtwo reference blocks which have been motion compensated, and decodes acurrent block using the at least one BIO parameter calculated.

FIG. 52 is a flow chart indicating the third specific example of thedecoding process based on BIO.

First, decoder 200 calculates a first sum for the current block, usingthe horizontal gradient value of a first reference block and thehorizontal gradient value of a second reference block (S2001). The firstsum calculation process (S2001) in the specific example may be the sameas the first sum calculation process (S1001) in the first specificexample. Specifically, decoder 200 calculates sG_(x) as the first sumaccording to Expressions (6.1) and (6.2) which are the same asExpressions (3.1) and (3.2) in the first specific example.

[Math. 38]

G _(x) =I _(x) ⁰ +I _(x) ¹  (6.1)

[Math. 39]

sG _(x)=Σ_([i,j]∈Ω)sign(G _(x)[i,j])×G _(x)[i,j]  (6.2)

In addition, decoder 200 calculates a second sum for the current block,using a vertical gradient value of the first reference block and avertical gradient value of the second reference block (S2002). Thesecond sum calculation process (S2002) in the specific example may bethe same as the second sum calculation process (S1002) in the firstspecific example. Specifically, decoder 200 calculates sG_(y) as thesecond sum according to Expressions (6.3) and (6.4) which are the sameas Expressions (3.3) and (3.4) in the first specific example.

[Math. 40]

G _(y) =I _(y) ⁰ +I _(y) ¹  (6.3)

[Math. 41]

sG _(y)=Σ_([i,j]∈Ω)sign(G _(y)[i,j])×G _(y)[i,j]  (6.4)

Next, decoder 200 judges whether at least one of the followingconditions is satisfied: both the first sum and the second sum arelarger than a first value; and both the first sum and the second sum aresmaller than a second value (S2003). The first value may be larger thanthe second value, smaller than the second value, or the same as thesecond value. The first value and the second value may be represented asa first threshold value and a second threshold value, respectively.

For example, when the first value=100 and the second value=100 aresatisfied, judgement results based on the first sum and the second sumare as indicated below.

The first sum=300, and the second sum=50: The judgement result is false.

The first sum=50, and the second sum=50: The judgement result is true.

The first sum=300, and the second sum=300: The judgement result is true.

The first sum=50, and the second sum=300: The judgement result is false.

When a judgement result is true (Yes in S2003), decoder 200 determinestwo BIO parameters for a current block using both horizontal gradientvalues and vertical gradient values (S2004). Expressions (6.5) to (6.8)indicate an example of a computation process for determining two BIOparameters in this case. According to these expressions, the two BIOparameters denoted as u and v are calculated using the horizontalgradient values and the vertical gradient values.

[Math. 42]

sG _(x) dI=Σ _([i,j]∈Ω)sign(G _(x)[i,j])×(I ⁰ _(i,j) −I ¹ _(i,j))  (6.5)

[Math. 43]

sG _(y) dI=Σ _([i,j]∈Ω)sign(G _(y)[i,j])×(I ⁰ _(i,j) −I ¹ _(i,j))  (6.6)

[Math. 44]

u=Clip(((sG _(x) dI>>(Bits(sG _(x))−6−12))×BIOShift[sG _(x)>>>Bits(sG_(x))−6])>>27)  (6.7)

[Math. 45]

V=Clip(((sG _(y) dI)(Bits(sG _(y))−6−12))×BIOShift[sG _(y)>>>Bits(sG_(y))−6])>27)  (6.8)

Expressions (6.5) and (6.6) are the same as Expressions (3.5) and (3.10)in the first specific example, respectively. BIO parameter u is derivedusing sG_(x)dI and sGx according to Expression (6.7). BIO parameter v iscalculated using sG_(y)dI and sGy according to Expression (6.8). BIOparameters u and v may be calculated using Expressions (6.9) and (6.10)indicated below, respectively, instead of using Expressions (6.7) and(6.8), respectively.

[Math. 46]

u=sG _(x) dI>>Bits(sG _(x))  (6.9)

[Math. 47]

v=sG _(y) dI>>Bits(sG _(y))  (6.10)

When a judgement result is false (No in S2003), decoder 200 determinesone BIO parameter for a current block without using either horizontalgradient values or vertical gradient values (S2005). The example of acomputation process for determining the one BIO parameter in this caseis indicated below.

For example, decoder 200 judges whether the first sum is larger than thesecond sum. In the case where the first sum is larger than the secondsum, decoder 200 calculates only “u” as the BIO parameter according toExpressions (6.5) and (6.7) (or (6.9)). In other words, in this case,decoder 200 determines the BIO parameter for the current block withoutusing the vertical gradient values.

In the opposite case where the first sum is not larger than the secondsum, decoder 200 calculates only “v” as the BIO parameter according toExpressions (6.6) and (6.8) (or (6.10)). In other words, in this case,decoder 200 determines the BIO parameter for the current block withoutusing the horizontal gradient values.

Alternatively, for example, decoder 200 may judge whether the first sumis larger than the first value and the second sum is smaller than thesecond value.

When the first sum is larger than the first value and the second sum issmaller than the second value, decoder 200 may then determine only “u”as the BIO parameter for the current block without using the verticalgradient values. When the first sum is not larger than the first valueand the second sum is not smaller than the second value, decoder 200 maythen determine only “v” as the BIO parameter for the current blockwithout using the horizontal gradient values.

Lastly, decoder 200 then decodes the current block using at least oneBIO parameter (S2006). Specifically, decoder 200 generates a predictionsample using at least one of BIO parameters u and v, and decodes thecurrent block using the prediction sample. Expressions (6.11) to (6.13)indicate an example of a computation process for generating a predictionsample.

[Math. 48]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (6.11)

[Math. 49]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹))>>1  (6.12)

[Math. 50]

prediction sample=(I ⁰ +I ¹ +v×(I _(y) ⁰ −I _(y) ¹))>>1  (6.13)

When the judgement result based on the first sum, the second sum, thefirst value, and the second value (S2003) is true, Expression (6.11) isused. In the case where only “u” is calculated when the judgement result(S2003) is false, Expression (6.12) is used. In the case where only “v”is calculated when the judgement result (S2003) is false, Expression(6.13) is used.

Decoder 200 may repeat the processes (S2001 to S2006) for all thesub-blocks in each of current CUs.

In addition, a judgement process different from the judgement process(S2003) described above may be used. For example, decoder 200 may judgewhether both the first sum and the second sum are larger than the firstvalue.

In the case where both the first sum and the second sum are larger thanthe first value, decoder 200 may then determine two BIO parameters for acurrent block using both horizontal gradient values and verticalgradient values. In the case where at least one of the first sum and thesecond sum is not larger than the first value, decoder 200 may determineone BIO parameter for a current block without using either horizontalgradient values and vertical gradient values.

Alternatively, for example, decoder 200 may judge whether the first sumis larger than the first value and the second sum is smaller than thesecond value.

In the case where the first sum is larger than the first value and thesecond sum is larger than the second value, decoder 200 may thendetermine two BIO parameters for a current block using both horizontalgradient values and vertical gradient values. In the case where thefirst sum is not larger than the first value or the second sum is notlarger than the second value, decoder 200 may then determine one BIOparameter for a current block without using any horizontal gradientvalue or any vertical gradient value.

Alternatively, for example, decoder 200 may determine whether at leastone of the following conditions is satisfied: the first sum is largerthan the first value and the second sum is larger than the second value;and the first sum is smaller than a third value and the second sum issmaller than a fourth value.

When at least one of the two conditions is satisfied, decoder 200 maythen determine two BIO parameters for the current block using bothhorizontal gradient values and vertical gradient values. When any of thetwo conditions is not satisfied, decoder 200 may determine one BIOparameter for the current block without using either any horizontalgradient value or any vertical gradient value.

Decoder 200 is capable of increasing the accuracy of the predictionsample in the current block using BIO. In addition, decoder 200 may useonly one of horizontal gradient values and vertical gradient valuesbased on a condition. In this way, decoder 200 is capable of reducingincrease in the amount of computation.

The above expressions are examples, and expressions for calculating aBIO parameter are not limited to the above expressions. For example, theplus or minus sign included in each expression may be changed, or anexpression equivalent to any of the above expressions may be used.Specifically, as an expression corresponding to Expressions (6.1) and(6.2) described above, following Expression (7.1) may be used.

[Math. 51]

sG _(x)=Σ_([i,j]∈Ω)abs(I _(x) ¹ +I _(x) ⁰)  (7.1)

In addition, for example, as an expression corresponding to Expression(6.5) described above, following Expression (7.2) may be used.

[Math. 52]

sG _(x) dI=Σ _([i,j]∈Ω)(−sign(I _(x) ¹ +I _(x) ⁰)×(I ⁰ −I ¹))  (7.2)

For example, as an expression corresponding to Expression (6.12)described above, following Expression (7.3) may be used.

[Math. 53]

prediction sample=(I ¹ +I ⁰ −u×(I _(x) ¹ −I _(x) ⁰))>>1  (7.3)

Expressions (6.7) and (6.9) substantially indicate division, and thusmay be represented as following Expression (7.4).

[Math.  54] $\begin{matrix}{u = \frac{{sG}_{x}{dI}}{{sG}_{x}}} & (7.4)\end{matrix}$

Expressions (7.1) to (7.4) are substantially the same as Expressions(6.1), (6.2), (6.5), (6.7), (6.9), and (6.12) described above.

Likewise, specifically, as an expression corresponding to Expressions(6.3) and (6.4) described above, following Expression (7.5) may be used.

[Math. 55]

sG _(y)=Σ_([i,j]∈Ω)abs(I _(y) ¹ +I _(y) ⁰)  (7.5)

In addition, for example, as an expression corresponding to Expression(6.6) described above, following Expression (7.6) may be used.

[Math. 56]

sG _(y) dI=Σ _([i,j]∈Ω)(−sign(I _(y) ¹ +I _(y) ⁰)×(I ⁰ −I ¹))  (7.6)

For example, as an expression corresponding to Expression (6.13)described above, following Expression (7.7) may be used.

[Math. 57]

prediction sample=(I ¹ +I ⁰ −v×(I _(y) ¹ −I _(y) ⁰))>>1  (7.7)

Expressions (6.8) and (6.10) substantially indicate division, and thusmay be represented as following Expression (7.8).

[Math.  58] $\begin{matrix}{u = \frac{{sG}_{y}{dI}}{{sG}_{y}}} & (7.8)\end{matrix}$

Expressions (7.5) to (7.8) are substantially the same as Expressions(6.3), (6.4), (6.6), (6.8), (6.10), and (6.13) described above. Forexample, as an expression corresponding to Expression (6.11) describedabove, following Expression (7.9) may be used. Following Expression(7.9) is substantially the same as Expression (6.11) described above.

[Math. 59]

prediction sample=(I ⁰ +I ¹ −u×(I _(x) ¹ −I _(x) ⁰)−v×(I _(y) ¹ −I _(y)⁰))>>1  (7.9)

In addition, in the above flow, at least one of the horizontal gradientvalues and the vertical gradient values are used based on the first sumand the second sum in the above flow, flows of a decoding process arenot limited to the above-described flow. It is also excellent thatwhether to use the horizontal gradient values, the vertical gradientvalues, or both the horizontal gradient values and the vertical gradientvalues may be defined by another coding parameter, or the like.

Regardless of a first sum and a second sum, at least one BIO parametermay be derived using the horizontal gradient values, the verticalgradient values, or both the horizontal gradient values and the verticalgradient values.

Regardless of the first sum and the second sum, according to theexpressions described above, decoder 200 is capable of reducingsubstantial multiplication which requires a large amount of computationin the computations performed for the respective pixel positions, andderiving a plurality of parameters for generating the prediction imagewith a small amount of computation. Specifically, although the plus orminus signs in Expressions (6.2), (6.4), (6.5), (6.6), (7.1), (7.2),(7.5), (7.6), etc. are changed, no substantial multiplication is used.Accordingly, the number of times of substantial multiplication in BIOprocessing can be reduced significantly.

In other words, decoder 200 is capable of calculating sG_(x), sG_(x)dI,sG_(y), and sG_(y)dI with a small amount of computation. Accordingly,decoder 200 is capable of reducing the processing amount in decoding. Inparticular, regardless of the first sum and the second sum, decoder 200may derive at least one BIO parameter using both horizontal gradientvalues and vertical gradient values. In this way, decoder 200 is capableof appropriately generating a prediction image using both the horizontalgradient value and the vertical gradient value while reducing theprocessing amount in decoding.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

It is to be noted that expressions for calculating a BIO parameter maybe replaced with other expressions as long as the other expressions areused to calculate the BIO parameter using either horizontal gradientvalues or vertical gradient values.

For example, in the third specific example, expressions for calculatingBIO parameter u are not limited to Expressions (6.7), (6.9), (7.4), etc.and may be other expressions as long as the other expressions are usedto calculate BIO parameter u based on horizontal gradient values andwithout being based on vertical gradient values. In addition,expressions for calculating BIO parameter v are not limited toExpressions (6.8), (6.10), (7.8), etc. and may be other expressions aslong as the other expressions are used to calculate BIO parameter vbased on vertical gradient values and without being based on horizontalgradient values.

In addition, in the first specific example and the third specificexample, the first sum corresponds to horizontal gradient values and thesecond sum corresponds to vertical gradient values. However, the ordermay be inversed. In other words, the first sum may correspond tovertical gradient values and the second sum may correspond to horizontalgradient values.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, or a BIO parameter maybe replaced with one or more of expressions in the other specificexamples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

[Fourth Specific Example of BIO]

The BIO parameter calculation processes and the prediction imagegeneration processes in the first specific example, the second specificexample, and the third specific example are examples, and othercalculation processes and other generation processes may be applied. Forexample, the process indicated in the flow chart in FIG. 53 may beapplied.

FIG. 53 is a flow chart indicating a fourth specific example of thedecoding process based on BIO. In the plurality of specific examplesdescribed above, decoder 200 switches methods of deriving a predictionsample based on the magnitude of the first sum and the magnitude of thesecond sum, as indicated in FIGS. 49 and 52. In comparison, in thisspecific example, decoder 200 always calculates an optical flowcomponent in a vertical direction and a horizontal direction to derive aprediction sample. This produces a possibility of further increasingprediction accuracy.

Specifically, in an example in FIG. 53 similarly to the example in FIG.49 and the example in FIG. 52, decoder 200 calculates a first sum for acurrent block, using a horizontal gradient value of a first referenceblock and a horizontal gradient value of a second reference block(S2001). In addition, decoder 200 calculates a second sum for thecurrent block, using a vertical gradient value of the first referenceblock and a vertical gradient value of the second reference block(S2002).

In the example of FIG. 53, decoder 200 then determines a BIO parameterfor the current block using both the horizontal gradient values and thevertical gradient values regardless of the magnitude of the first sumand the magnitude of the second sum (S2004). The operation fordetermining the BIO parameter for the current block using both thehorizontal gradient values and the vertical gradient values may be thesame as the operation in the third specific example. For example,decoder 200 may use Expressions (6.1) to (6.10) described in the thirdspecific example as computation expressions for determining a BIOparameter.

Decoder 200 then decodes the current block using the BIO parameter(S2006). For example, decoder 200 generates a prediction sample usingtwo BIO parameters u and v. At that time, decoder 200 may derive theprediction sample according to Expression (6.11), etc. Decoder 200 mayuse the expressions described in the first specific example or otherexpressions. Decoder 200 then decodes the current block using theprediction sample.

In addition, sign (x) appeared in Expressions (6.2), (6.4), (6.5),(6.6), etc. may be defined by binary Expression (a) described above, ormay be defined by following Expression (b).

[Math.  60] $\begin{matrix}{{{sign}(x)} = \{ \begin{matrix}1 & {{{if}\mspace{14mu} x} > 0} \\0 & {{{if}\mspace{14mu} x} = 0} \\{- 1} & {{{if}\mspace{14mu} x} < 0}\end{matrix} } & (b)\end{matrix}$

In Expression (a), the sign function returns a value indicating whetheran argument provided to the sign function is a plus value or a minusvalue. In Expression (b), the sign function returns a value indicatingwhether an argument provided to the sign function is a plus value, aminus value, or 0.

In the original optical flow derivation expressions, sign (G_(x) [i, j])and sign (G_(y) [i, j]) in Expressions (6.2), (6.4), (6.5), and (6.6)are G_(x) [i, j] and G_(y) [i, j], respectively. Accordingly, forexample, G_(x) [i, j]×(I⁰ _(i,j)−I¹ _(i, j))=0 is calculated as anintermediate value when G_(x) [i, j]=0 is satisfied, and G_(y) [i,j]×(I⁰ _(i,j)−I¹ _(i,j))=0 is calculated as an intermediate value whenG_(y) [i, j]=0 is satisfied.

However, in the simplified optical flow derivation expressions, anyappropriate intermediate value can be obtained when sign (0)=1 issatisfied. For example, in Expression (6.5), sign (G_(x) [i, j])×(I⁰_(i,j)−I¹ _(i, j))=(I⁰ _(i, j)−I¹ _(i, j)) is calculated as anintermediate value when G_(x) [i, j]=0 is satisfied. For example, inExpression (6.6), sign (G_(y) [i, j])×(I⁰ _(i, j)−I¹ _(i, j))=(I⁰_(i, j)−I¹ _(i, j)) is calculated as an intermediate value when G_(y)[i, j]=0 is satisfied. In other words, the intermediate value is not 0,and a value different from 0 remains.

In the definition of sign in Expression (b) described above, sign (G_(x)[i, j])×(I⁰ _(i, j)−I¹ _(i, j))=(I⁰ _(i, j)−I¹ _(i, j)) is calculated asthe intermediate value when G_(x) [i, j]=0 is satisfied, and sign (G_(x)[i, j])×(I⁰ _(i, j)−I¹ _(i, j))=(I⁰ _(i, j)−I¹ _(i, j)) is calculated asthe intermediate value when G_(x) [i, j]=0 is satisfied. Accordingly, inthese cases, the same intermediate values as in the original opticalflow derivation expressions are calculated.

Thus, the sign defined by Expression (b) described above has a valuecloser to the value obtainable in the original optical flow expressionthan the sign defined by Expression (a) described above. Accordingly,this produces a possibility of further increasing prediction accuracy.

It is to be noted that the above modifications may be combined entirelyin the present disclosure. For example, the definition of sign (x) inthe first specific example may be replaced with Expression (b) describedabove, or the definition of sign (x) in the third specific example maybe replaced with Expression (b) described above.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description,for example, a filter having a filter coefficient set of [1, 0, −1] maybe used instead.

Expression (b) is one example of a sign function that returns a valueindicating whether an argument indicates a plus value, a minus value, or0. The sign function that provides a value indicating whether anargument indicates a plus value, a minus value, or 0 may be representedaccording to another expression that can take a value depending onwhether an argument indicates a plus value, a minus value, or 0 fromamong the three possible values.

[Fifth Specific Example of BIO]

Next, a fifth specific example of a decoding process based on BIO isdescribed. In the fifth specific example, an optical flow component isalways calculated in a vertical direction and a horizontal direction sothat a prediction sample is calculated as in the fourth specificexample. The following computation expressions are computationexpressions in the fifth specific example.

[Math. 61]

G _(x) =I _(x) ⁰ +I _(x) ¹  (8.1)

[Math. 62]

sG _(x)=Σ_([i,j]∈Ω)sign(G _(x)[i,j])×G _(x)[i,j]  (8.2)

[Math. 63]

G _(y) =I _(y) ⁰ +I _(y) ¹  (8.3)

[Math. 64]

sG _(y)=Σ_([i,j]∈Ω)sign(G _(y)[i,j])×G _(y)[i,j]  (8.4)

[Math. 65]

sG _(x) dI=Σ _([i,j]∈Ω)sign(G _(x)[i,j])×(I ⁰ _(i,j) −I ¹ _(i,j))  (8.5)

[Math. 66]

sG _(y) dI=Σ _([i,j]∈Ω)sign(G _(y)[i,j])×(I ⁰ _(i,j) −I ¹ _(i,j))  (8.6)

[Math. 67]

sG _(x) G _(y)=Σ_([i,j]∈Ω)sign(G _(y)[i,j])×G _(x)[i,j]  (8.7)

[Math. 68]

u=sG _(x) dI>>>Bits(sG _(x))  (8.8)

[Math. 69]

v=(sG _(y) dI−u×sG _(x) G _(y))>>Bits(sG _(y))  (8.9)

[Math. 70]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (8.10)

Expressions (8.1) to (8.6), (8.8), and (8.10) are the same asExpressions (6.1) to (6.6), (6.9), and (6.11) in the third specificexample. In the specific example, Expression (8.7) is added, andExpression (6.10) is replaced with Expression (8.9). In other words, BIOparameter “v” in the y direction is derived through a computationprocess that depends on BIO parameter “u” in the x direction and acorrelation parameter “sG_(x)G_(y)” which indicates a correlationbetween the gradient in the x direction and the gradient in the ydirection. This makes it possible to derive a BIO parameter with ahigher accuracy, which increases the possibility of being able toincrease coding efficiency. It is to be noted that sG_(x)G_(y) can berepresented as a third sum.

In addition, Expression (b) described in the fourth specific example maybe used as sign (x). As defined in Expression (b), there is apossibility of being able to further increase coding efficiency by sign(x) corresponding to three values. In addition, Expression (a) describedin the first specific example may be used as sign (x). This simplifiesthe expression compared to the case where sign (x) corresponds to threevalues, which produces a possibility of being able to increase codingefficiency while reducing processing load.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, a third sum, or a BIOparameter may be replaced with one or more of expressions in the otherspecific examples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

The computation expression may be applied not only to the flow chart inFIG. 53 in the fourth specific example, but also to the flow chart inFIG. 49 in the first specific example, the flow chart in FIG. 52 in thethird specific example, and other flow charts.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

[Sixth Specific Example of BIO]

Next, a sixth specific example of a decoding process based on BIO isdescribed. In the sixth specific example, an optical flow component isalways calculated in a vertical direction and a horizontal direction sothat a prediction sample is calculated as in the fourth specificexample, etc. The following computation expressions are computationexpressions in the sixth specific example.

[Math. 71]

G _(x) =I _(x) ⁰ +I _(x) ¹  (9.1)

[Math. 72]

sG _(x)=Σ_([i,j]∈Ω) G _(x)[i,j]×G _(x)[i,j]  (9.2)

[Math. 73]

G _(y) =I _(y) ⁰ +I _(y) ¹  (9.3)

[Math. 74]

sG _(y)=Σ_([i,j]∈Ω) G _(y)[i,j]×G _(y)[i,j]  (9.4)

[Math. 75]

sG _(x) dI=Σ _([i,j]∈Ω) G _(x)[i,j]×(I ⁰ _(i,j) −I ¹ _(i,j))  (9.5)

[Math. 76]

sG _(y) dI=Σ _([i,j]∈Ω) G _(y)[i,j]×(I ⁰ _(i,j) −I ¹ _(i,j))  (9.6)

[Math. 77]

u=sG _(x) dI>>Bits(sG _(x))  (9.7)

[Math. 78]

v=sG _(y) dI>>Bits(sG _(u))  (9.8)

[Math. 79]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (9.9)

Expressions (9.1), (9.3), and (9.7) to (9.9) are the same as Expressions(6.1), (6.3), and (6.9) to (6.11) in the third specific example. In thisspecific example, Expressions (6.2) and (6.4) to (6.6) are replaced withExpressions (9.2) 20 and (9.4) to (9.6), respectively.

For example, in Expressions (6.2) and (6.4) to (6.6), sign (G_(x) [i,j]) and sign (G_(y) [i, j]) is used instead of G_(x) [i, j] and G_(y)[i, j], and substantial multiplication is removed. In contrast, inExpressions (9.2) and (9.4) to (9.6), sign (G_(x) [i, j]) and sign(G_(y) [i, j]) are not used, and the values of G_(x) [i, j] and G_(y)[i, j] are directly used. In other words, substantial multiplication isused.

This increases computation processing amount. However, this makes itpossible to derive a BIO parameter with a higher accuracy, whichincreases the possibility of being able to increase coding efficiency.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, a third sum, or a BIOparameter may be replaced with one or more of expressions in the otherspecific examples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

The computation expression corresponding to this specific example may beapplied not only to the flow chart in FIG. 53 in the fourth specificexample, but also to the flow chart in FIG. 49 in the first specificexample, the flow chart in FIG. 52 in the third specific example, andother flow charts.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

[Seventh Specific Example of BIO]

Next, a seventh specific example of a decoding process based on BIO isdescribed. In the seventh specific example, an optical flow component isalways calculated in a vertical direction and a horizontal direction sothat a prediction sample is calculated as in the fourth specificexample, etc. The following computation expressions are computationexpressions in the seventh specific example.

[Math. 80]

G _(x) =I _(x) ⁰ +I _(x) ¹  (10.1)

[Math. 81]

sG _(x)=Σ_([i,j]∈Ω)abs(G _(x)[i,j])  (10.2)

[Math. 82]

G _(y) =I _(y) ⁰ +I _(y) ¹  (10.3)

[Math. 83]

sG _(y)=Σ_([i,j]∈Ω)abs(G _(y)[i,j])  (10.4)

[Math. 84]

sG _(x) dI=Σ _([i,j]∈Ω)sign(G _(x)[i,j])×(I ⁰ _(i,j) −I ¹_(i,j))  (10.5)

[Math. 85]

sG _(y) dI=Σ _([i,j]∈Ω)sign(G _(y)[i,j])×(I ⁰ _(i,j) −I ¹_(i,j))  (10.6)

[Math. 86]

sG _(x) G _(y)=Σ_([i,j]∈Ω)sign(G _(y)[i,j])×G _(x)[i,j]  (10.7)

[Math. 87]

u=sG _(x) dI>>Bits(sG _(x))  (10.8)

[Math. 88]

v=(sG _(y) dI−u×sG _(x) G _(y))>>Bits(sG _(y))  (10.9)

[Math. 89]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (10.10)

Expressions (10.1), (10.3), and (10.5) to (10.10) are the same asExpressions (8.1), (8.3), and (8.5) to (8.10) in the fifth specificexample. In this specific example, Expressions (8.2) and (8.4) arereplaced with Expressions (10.2) and (10.4), respectively. Specifically,an abs function is used instead of a sign function for transforming aplus or minus sign.

The results obtainable using abs functions as in Expressions (10.2) and(10.4) are the same as the results obtainable by transforming the plusor minus functions using sign functions as in Expressions (8.2) and(8.4). In other words, this specific function is substantially the sameas the fifth specific example.

In the fifth specific example, the product of the plus or minus sign ofG_(x) and G_(x) is used, and the product of the plus or minus sign ofG_(y) and G_(y) is used. In this specific example, the product parts arereplaced with absolute values. This may achieve low-amount processing.

For example, the plus or minus sign included in each expression may bechanged as necessary, or an expression equivalent to any of the aboveexpressions may be used. Specifically, as expressions corresponding toExpressions (10.1) to (10.7) described above, following Expression(11.1) to (11.5) may be used.

[Math. 90]

sG _(x)=Σ_([i,j]∈Ω)abs(I _(x) ¹ +I _(x) ⁰)  (11.1)

[Math. 91]

sG _(y)=Σ_([i,j]∈Ω)abs(I _(y) ¹ +I _(y) ⁰)  (11.2)

[Math. 92]

sG _(x) dI=Σ _([i,j]∈Ω)(−sign(I _(x) ¹ +I _(x) ⁰)×(I ⁰ −I ¹))  (11.3)

[Math. 93]

sG _(y) dI=Σ _([i,j]∈Ω)(−sign(I _(y) ¹ +I _(y) ⁰)×(I ⁰ −I ¹))  (11.4)

[Math. 94]

sG _(x) G _(y)=Σ_([i,j]∈Ω)(sign(I _(y) ¹ +I _(y) ⁰)×(I _(x) ¹ +I _(x)⁰))  (11.5)

Expressions (10.8) and (10.9) substantially indicate division, and thusmay be represented as following Expressions (11.6) and (11.7).

[Math.  95] $\begin{matrix}{u = \frac{{sG}_{x}{dI}}{{sG}_{x}}} & \; & {\mspace{436mu}(11.6)}\end{matrix}\lbrack {{Math}.\mspace{14mu} 96} \rbrack$$\begin{matrix}{u = \frac{{{sG}_{x}{dI}} - {u \times {sG}_{x}G_{y}}}{{sG}_{y}}} & \; & {\mspace{304mu}(11.7)}\end{matrix}$

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, a third sum, or a BIOparameter may be replaced with one or more of expressions in the otherspecific examples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

The computation expression corresponding to this specific example may beapplied not only to the flow chart in FIG. 53 in the fourth specificexample, but also to the flow chart in FIG. 49 in the first specificexample, the flow chart in FIG. 52 in the third specific example, andother flow charts.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

[Eighth Specific Example of BIO]

Next, an eighth specific example of a decoding process based on BIO isdescribed. In the eighth specific example, an optical flow component isalways calculated in a vertical direction and a horizontal direction sothat a prediction sample is calculated as in the fourth specificexample, etc. The following computation expressions are computationexpressions in the eighth specific example.

[Math. 97]

G _(x) =I _(x) ⁰ +I _(x) ¹  (12.1)

[Math. 98]

sG _(x)=Σ_([i,j]∈Ω) G _(x)[i,j]  (12.2)

[Math. 99]

G _(y) =I _(y) ⁰ +I _(y) ¹  (12.3)

[Math. 100]

sG _(y)=Σ_([i,j]∈Ω) G _(y)[i,j]  (12.4)

[Math. 101]

sG _(X) dI=Σ _([i,j]∈Ω)(I ⁰ _(i,j) −I ¹ _(i,j))  (12.5)

[Math. 102]

sG _(y) dI=Σ _([i,j]∈Ω)(I ⁰ _(i,j) −I ¹ _(i,j))  (12.6)

[Math. 103]

sG _(x) G _(y)=Σ_([i,j]∈Ω) G _(x)[i,j]  (12.7)

[Math. 104]

u=sG _(x) dI>>Bits(sG _(x))  (12.8)

[Math. 105]

v=(sG _(y) dI−u×sG _(x) G _(y))>>Bits(sG _(y))  (12.9)

[Math. 106]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(x) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (12.10)

Expressions (12.1), (12.3), and (12.8) to (12.10) are the same asExpressions (8.1), (8.3), and (8.8) to (8.10) in the fifth specificexample.

On the other hand, regarding Expressions (8.2) and (8.4) to (8.7): thevalues indicating the plus or minus signs of G_(x) and G_(y) are alwaysassumed to be 1; and Expressions (8.2) and (8.4) to (8.7) are replacedwith Expressions (12.2) and (12.4) to (12.7), respectively. This isbased on the assumption that both the absolute values of the gradientvalues of pixel values and the plus or minus signs are constant in minerarea Ω.

Since it is assumed that the plus or minus signs are constant, a processof calculating the plus or minus signs of G_(x) and G_(y) for each pairof pixels can be reduced. In addition, the computation expression ofsG_(x) and the computation expression of sG_(x)G_(y) are equal to eachother. This enables further reduction in processing.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, a third sum, or a BIOparameter may be replaced with one or more of expressions in the otherspecific examples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1]is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

The computation expression may be applied not only to the flow chart inFIG. 53 in the fourth specific example, but also to the flow chart inFIG. 49 in the first specific example, the flow chart in FIG. 52 in thethird specific example, and other flow charts.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

[Ninth Specific Example of BIO]

Next, a ninth specific example of a decoding process based on BIO isdescribed. In the ninth specific example, an optical flow component isalways calculated in a vertical direction and a horizontal direction sothat a prediction sample is calculated as in the fourth specificexample, etc. The following computation expressions are computationexpressions in the ninth specific example.

[Math. 107]

G _(x) =I _(x) ⁰ +I _(x) ¹  (13.1)

[Math. 108]

sG _(x)=Σ_([i,j]∈Ω) G _(x)[i,j]  (13.2)

[Math. 109]

G _(y) =I _(y) ⁰ +I _(y) ¹  (13.3)

[Math. 110]

sG _(y)=Σ_([i,j]∈Ω) G _(y)[i,j]  (13.4)

[Math. 111]

sG _(y) dI=Σ _([i,j]∈Ω)(I ⁰ _(i,j) −I ¹ _(i,j))  (13.5)

[Math. 112]

sG _(y) dI=Σ _([i,j]∈Ω)(I ⁰ _(i,j) −I ¹ _(i,j))  (13.6)

[Math. 113]

u=sG _(y) dI>>Bits(sG _(x))  (13.7)

[Math. 114]

v=(sG _(y) dI−u×sG _(x))>>Bits(sG _(y))  (13.8)

[Math. 115]

prediction sample=(I ⁰ +I ¹ +u×(I _(x) ⁰ −I _(y) ¹)+v×(I _(y) ⁰ −I _(y)¹))>>1  (13.9)

Expressions (13.1) to (13.9) are the same as Expressions (12.1) to(12.6) and (12.8) to (12.10) in the eighth specific example. Based onthe equalness of the computation expression of sG_(x) and thecomputation expression of sG_(x)G_(y) in the eighth specific example, aprocess of deriving a cross correlation in a third sum is removed inthis specific example. To derive v, sG_(x) is used.

It is to be noted that the computation expressions described here areexamples. The computation expressions may be partially modified, partsof the expressions may be deleted, or parts may be added to theexpressions, as long as the resulting expressions are for performingsimilar processing. For example, one or more of a plurality ofexpressions related to a first sum, a second sum, or a BIO parameter maybe replaced with one or more of expressions in the other specificexamples, or may be replaced with other one or more expressionsdifferent from the expressions in the other specific examples.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

The computation expression corresponding to this specific example may beapplied not only to the flow chart in FIG. 53 in the fourth specificexample, but also to the flow chart in FIG. 49 in the first specificexample, the flow chart in FIG. 52 in the third specific example, andother flow charts.

Although the decoding process has been described in the abovedescription, the same processes included in the decoding process may beapplied also in an encoding process. In other words, the decoding in theabove description may be read as encoding.

[Tenth Specific Example of BIO]

This specific example indicates a variation example that is applicableto other specific examples. For example, a lookup table may be used fordivision in each specific example. For example, a 6-bit lookup tablehaving 64 entries (divSigTable) may be used. Expressions (8.8) and (8.9)in the fifth specific example can be replaced with following Expressions(14.1) and (14.2), respectively. The same-kind expressions in the otherspecific examples may be replaced in the same manner.

[Math. 116]

u=sG _(x) dI×(divSigTalbe[Upper6digits(sG _(x))]|32)>>[log(sG_(x))]  (14.1)

[Math. 117]

v=(sG _(y) dI−u×sG _(x))×(divSigTalbe[Upper6digits(sG _(y))]|32)>>└log(sG _(y))┘  (14.2)

Upper6digits in Expressions (14.1) and (14.2) described above representsthe following.

[Math. 118]

Upper6digits(Z)=(Z<<6)>>┌log(Z)┘&63  (14.3)

In addition, a gradient image is obtained by calculating gradient valuesof a plurality of pixels. The gradient values may be derived by, forexample, applying a gradient filter to the plurality of pixels.Increasing the number of taps of the gradient filter may increase theaccuracy of the gradient values, increase the accuracy of the predictionimage, and increase coding efficiency.

On the other hand, since the processing is performed for each pair ofpixel positions, the computation amount increases when the number ofpairs of pixel positions to be processed is large. Thus, a two-tapfilter may be used as a gradient filter. In other words, the gradientvalue may be a difference value between two pixels located above orbelow, or to the right or to the left of the target pair of pixels forwhich a gradient value is to be calculated. Alternatively, the gradientvalue may be a difference value between each of the target pair ofpixels for which the gradient value is to be calculated and aneighboring pixel that neighbors the target pixel (the neighboring pixelis specifically, the pixel located above or below, or to the right or tothe left of the target pixel). This may produce the possibility ofreducing the processing amount compared to the case where the number oftaps is large.

It is to be noted that the plurality of pixels for which gradient valuesare to be calculated may be a plurality of integer pixels, or mayinclude sub-pixels.

In addition, although the filter having a filter coefficient set of [−1,0, 1] is used as an example of a filter for calculating a horizontalgradient value and a vertical gradient value in the above description, afilter having a filter coefficient set of [1, 0, −1] may be usedinstead.

[Representative Examples of Configurations and Processing]

Descriptions are given of representative examples of the configurationsof and processes performed by encoder 100 and decoder 200 describedabove. These representative examples mainly correspond to the fifthspecific example and the seventh specific example described above.

FIG. 54 is a flow chart indicating an operation performed by encoder100. For example, encoder 100 includes circuitry and memory connected tothe circuitry. The circuitry and memory included in encoder 100 maycorrespond to processor a1 and memory a2 illustrated in FIG. 40. Thecircuitry of encoder 100 performs the following steps in operation.

For example, the circuitry of encoder 100 may derive, for each of aplurality of pairs of relative pixel positions, the absolute value ofthe sum of the horizontal gradient values which indicates the absolutevalue of the sum of the horizontal gradient value at a relative pixelposition in the first range and the horizontal gradient value at arelative pixel position in the second range (S3101).

Here, the first range includes a first reference block in a currentblock, and the second range includes a second reference block in thecurrent block. Each of the plurality of pairs of relative pixelpositions is determined commonly and relatively for both the first rangeand the second range, and each pair of relative pixel positions iscomposed of a pixel position in the first range and a pixel position inthe second range.

In addition, the pixel position determined commonly and relatively forboth the first range and the second rage means the pixel positiondetermined for both the first range and the second range relatively inthe same manner. For example, when one absolute value of the sum of thehorizontal gradient values is calculated, the horizontal gradient valuesat the pixel positions which are relatively the same in the first rangeand the second range are used. More specifically, for example, oneabsolute value of the sum of horizontal gradient values is derived usingthe horizontal gradient value at the upper leftmost pixel position inthe first range and the horizontal gradient value at the upper leftmostpixel position in the second range.

The circuitry of encoder 100 then derives, as a first parameter, thetotal sum of a plurality of absolute values of the sums of horizontalgradient values derived respectively for the plurality of pairs ofrelative pixel positions (S3102).

Furthermore, the circuitry of encoder 100 derives, for each of theplurality of pairs of relative pixel positions, the absolute value ofthe sum of vertical gradient values which indicates the absolute valueof the sum of the vertical gradient value at the relative pixel positionin the first range and the vertical gradient value at the relative pixelposition in the second range (S3103).

The circuitry of encoder 100 then derives, as a second parameter, thetotal sum of a plurality of absolute values of the sums of verticalgradient values derived respectively for the plurality of pairs ofrelative pixel positions (S3104).

Furthermore, the circuitry of encoder 100 derives, for each of aplurality of pairs of relative pixel positions, a pixel difference valuewhich indicates the difference between the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range (S3105). For example, at this time,the circuitry of encoder 100 derives the pixel difference value with aplus or minus sign by subtracting one of the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range in each of the plurality of pairs ofrelative pixel positions from the other.

The circuitry of encoder 100 then inverts or maintains the plus or minussign of the pixel difference value derived for the pair of relativepixel positions, according to the plus or minus sign of the sum of thehorizontal gradient values, and derives a horizontal-related pixeldifference value (S3106). Here, the sum of the horizontal gradientvalues at each pair of relative pixel positions indicates the sum of thehorizontal gradient value at the relative pixel position in the firstrange and the horizontal gradient value at the relative pixel positionin the second range. The horizontal-related pixel difference valueindicates the pixel difference value having the plus or minus signinverted or maintained according to the plus or minus sign of the sum ofthe horizontal gradient values.

The circuitry of encoder 100 then derives, as a third parameter, thetotal sum of a plurality of horizontal-related pixel difference valuesderived respectively for the plurality of pairs of relative positions(S3107).

Furthermore, the circuitry of encoder 100 then inverts or maintains theplus or minus sign of the pixel difference value derived for each pairof relative pixel positions, according to the plus or minus sign of thesum of the vertical gradient values, and derives a vertical-relatedpixel difference value (S3108). Here, the sum of the vertical gradientvalues at the pair of relative pixel positions indicates the sum of thevertical gradient value at the relative pixel position in the firstrange and the vertical gradient value at the relative pixel position inthe second range. The vertical-related pixel difference value indicatesthe pixel difference value having the plus or minus sign inverted ormaintained according to the plus or minus sign of the sum of thevertical gradient values.

The circuitry of encoder 100 then derives, as a fourth parameter, thetotal sum of a plurality of vertical-related pixel difference valuesderived respectively for the plurality of pairs of relative pixelpositions (S3109).

In addition, the circuitry of encoder 100 inverts or maintains the plusor minus sign of the sum of the vertical gradient values derived for thepair of relative pixel positions, according to the plus or minus sign ofthe sum of the vertical gradient values, and derives a vertical-relatedsum of horizontal gradient values (S3110). Here, the vertical-relatedsum of the horizontal gradient values indicates a sum of the horizontalgradient values having the plus or minus sign inverted or maintainedaccording to the plus or minus sign of the sum of the vertical gradientvalues.

The circuitry of encoder 100 then derives, as a fifth parameter, thetotal sum of a plurality of vertical-related sums of horizontal gradientvalues derived respectively for the plurality of pairs of relative pixelpositions (S3111).

The circuitry of encoder 100 then generates a prediction image to beused to encode the current block using the first parameter, the secondparameter, the third parameter, the fourth parameter, and the fifthparameter (S3112).

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive a plurality of parametersfor generating a prediction image with a low amount of computation.Accordingly, the processing amount in encoding may be reduced. Inaddition, the prediction image may be generated appropriately, based onthe plurality of parameters including the parameter related to thehorizontal gradient values, the parameter related to the verticalgradient values, and the parameter related to both the horizontalgradient values and the vertical gradient values.

In addition, for example, the circuitry of encoder 100 may derive afirst parameter according to Expression (11.1) described above, and asecond parameter according to Expression (11.2) described above. Inaddition, for example, the circuitry of encoder 100 may derive a thirdparameter according to Expression (11.3) described above, and a fourthparameter according to Expression (11.4) described above. In addition,for example, the circuitry of encoder 100 may derive a fifth parameteraccording to Expression (11.5) described above.

Here, Ω denotes a set of relative pixel positions, and [i, j] denoteseach of the relative pixel positions. For each of the plurality of pairsof relative pixel positions, I_(x) ⁰ denotes a horizontal gradient valueat a relative pixel position in the first range, and I_(x) ¹ denotes ahorizontal gradient value at a relative pixel position in the secondrange. For each of the plurality of pairs of relative pixel positions,I_(y) ⁰ denotes a vertical gradient value at a relative pixel positionin the first range, and I_(y) ¹ denotes a vertical gradient value at arelative pixel position in the second range.

For each of the plurality of pairs of relative pixel positions, I⁰denotes a pixel value at the relative pixel position in the first range,and I¹ denotes a pixel value at the relative pixel position in thesecond range. In addition, abs (I_(x) ¹+I_(x) ⁰) denotes an absolutevalue of I_(x) ¹+I_(x) ⁰, and sign (I_(x) ¹+I_(x) ⁰) denotes a plus orminus sign of I_(x) ¹+I_(x) ⁰. Also, abs (I_(y) ¹+I_(y) ⁰) denotes anabsolute value of I_(y) ¹+I_(y) ⁰, and sign (I_(y) ¹+I_(y) ⁰) denotes aplus or minus sign of I_(y) ¹+I_(y) ⁰.

In this way, a plurality of parameters may be derived with a low amountof computation using pixel values, horizontal gradient values, andvertical gradient values.

In addition, for example, the circuitry of encoder 100 may derive asixth parameter by dividing the third parameter by the first parameter.In addition, the circuitry of encoder 100 may derive a seventh parameterby subtracting a product of the fifth parameter and the sixth parameterfrom the fourth parameter, and dividing a result of the subtraction bythe second parameter. The circuitry of encoder 100 may then generate theprediction image using the sixth parameter and the seventh parameter.

In this way, a plurality of parameters may be appropriately narroweddown to two parameters corresponding to the horizontal direction and thevertical direction. The parameter related to the horizontal gradientvalues may be appropriately incorporated in the parameter correspondingto the horizontal direction. The parameter related to the verticalgradient values, the parameter related to both the horizontal gradientvalues and the vertical gradient values, and the parameter related tothe horizontal gradient values may be appropriately incorporated in theparameter corresponding to the vertical direction. The prediction imagemay be appropriately generated using the two parameters.

In addition, for example, the circuitry of encoder 100 may derive asixth parameter according to Expression (10.8) described above. Inaddition, for example, the circuitry of encoder 100 may derive a seventhparameter according to Expression (10.9) described above.

Here, sG_(x) denotes the first parameter, sG_(y) denotes the secondparameter, sG_(x)dI denotes the third parameter, sG_(y)dI denotes thefourth parameter, sG_(x)G_(y) denotes the fifth parameter, and u denotesthe sixth parameter. Bits is a function which returns a value obtainableby rounding up a binary logarithm of an argument to an integer.

In this way, two parameters corresponding to the horizontal directionand the vertical direction may be derived with a low amount ofcomputation.

In addition, the circuitry of encoder 100 may generate the predictionimage by deriving a prediction pixel value, using: a first pixel value;a first horizontal gradient value; a first vertical gradient value; asecond pixel value; a second horizontal gradient value; a secondvertical gradient value; the sixth parameter; and the seventh parameter.

Here, the prediction pixel value is the prediction pixel value at theposition of a current pixel included in the current block. The firstpixel value is the first pixel value at a first pixel positioncorresponding to the position of the current pixel in the firstreference block. The first horizontal gradient value is a horizontalgradient value at the first pixel position. The first vertical gradientvalue is a vertical gradient value at the first pixel position. Thesecond pixel value is the pixel value at a second pixel positioncorresponding to the position of the current pixel in the secondreference block. The second horizontal gradient value is a horizontalgradient value at the second pixel position. The second verticalgradient value is a vertical gradient value at the second pixelposition.

This provides a possibility that the prediction image is generatedusing, for example, the two parameters corresponding to the horizontaldirection and the vertical direction, and the two parameterscorresponding to the horizontal direction and the vertical direction areappropriately reflected on the prediction image.

In addition, for example, the circuitry of encoder 100 may derive theprediction pixel value by dividing, by 2, a sum of the first pixelvalue, the second pixel value, a first correction value, and a secondcorrection value. Here, the first correction value corresponds to aproduct of a difference between the first horizontal gradient value andthe second horizontal gradient value and the sixth parameter, and thesecond correction value corresponds to a product of a difference betweenthe first vertical gradient value and the second vertical gradient valueand the seventh parameter.

In this way, a prediction image may be appropriately generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction.

In addition, for example, the circuitry of encoder 100 may derive aprediction pixel value according to Expression (10.10) described above.Here, I⁰ denotes the first pixel value, I¹ denotes the second pixelvalue, u denotes the sixth parameter, I_(x) ⁰ denotes the firsthorizontal gradient value, I_(x) ¹ denotes the second horizontalgradient value, v denotes the seventh parameter, I_(y) ⁰ denotes thefirst vertical gradient value, and I_(y) ¹ denotes the second verticalgradient value. In this way, a prediction image may be appropriatelygenerated according to an expression related to, for example, the twoparameters corresponding to the horizontal direction and the verticaldirection.

In addition, for example, the circuitry of encoder 100 may derive aparameter in a bi-directional optical flow using the first parameter,the second parameter, the third parameter, the fourth parameter, and thefifth parameter, and generate a prediction image using at least one ofthe parameters in the bi-directional optical flow and the bi-directionaloptical flow. In this way, encoder 100 is capable of appropriatelygenerating the prediction image.

At least one parameter in the bi-directional optical flow may be one ofthe sixth parameter and the seventh parameter described above.

It is to be noted that inter predictor 126 of encoder 100 may performthe operation described above as the circuitry of encoder 100.

FIG. 55 is a flow chart indicating an operation performed by decoder200. For example, decoder 200 includes circuitry and memory connected tothe circuitry. The circuitry and memory included in decoder 200 maycorrespond to processor b1 and memory b2 illustrated in FIG. 46. Thecircuitry of decoder 200 performs the following in operation.

For example, the circuitry of decoder 200 may calculate, for each of aplurality of pairs of relative pixel positions, the absolute value ofthe sum of the horizontal gradient values which indicates the absolutevalue of the sum of the horizontal gradient value at a relative pixelposition in the first range and the horizontal gradient value at arelative pixel position in the second range (S3201).

Here, the first range includes a first reference block in a currentblock, and the second range includes a second reference block in thecurrent block. Each of the plurality of pairs of relative pixelpositions is determined commonly and relatively for both the first rangeand the second range, and each pair of relative pixel positions iscomposed of a pixel position in the first range and a pixel position inthe second range.

The circuitry of decoder 200 then derives, as a first parameter, thetotal sum of a plurality of absolute values of the sums of gradientvalues derived respectively for the plurality of pairs of relativepositions (S3202).

Furthermore, the circuitry of decoder 200 calculates, for each of theplurality of pairs of relative pixel positions, the absolute value ofthe sum of the vertical gradient values which indicates the absolutevalue of the sum of the vertical gradient value at the relative pixelposition in the first range and the vertical gradient value at therelative pixel position in the second range (S3203).

The circuitry of decoder 200 then derives, as a second parameter, thetotal sum of a plurality of absolute values of the sums of gradientvalues derived respectively for the plurality of pairs of relativepositions (S3204).

In addition, the circuitry of decoder 200 derives a pixel differencevalue which is the difference between the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range, for each of the plurality of pairsof relative pixel positions (S3205). For example, at this time, thecircuitry of decoder 200 derives the pixel difference value with a plusor minus sign by subtracting one of the pixel value at the relativepixel position in the first range and the pixel value at the relativepixel position in the second range in each of the plurality of pairs ofrelative pixel positions from the other.

The circuitry of decoder 200 then inverts or maintains the plus or minussign of the pixel difference value derived for the pair of relativepixel positions, according to the plus or minus sign of the sum of thehorizontal gradient values, and derives a horizontal-related pixeldifference value (S3206). Here, the sum of the horizontal gradientvalues at each pair of relative pixel positions indicates the sum of thehorizontal gradient value at the relative pixel position in the firstrange and the horizontal gradient value at the relative pixel positionin the second range. The horizontal-related pixel difference valueindicates the pixel difference value having the plus or minus signinverted or maintained according to the plus or minus sign of the sum ofthe horizontal gradient values.

The circuitry of decoder 200 then derives, as a third parameter, thetotal sum of a plurality of horizontal-related pixel difference valuesderived respectively for the plurality of pairs of relative positions(S3207).

Furthermore, the circuitry of decoder 200 then inverts or maintains theplus or minus sign of the pixel difference value derived for each pairof relative pixel positions, according to the plus or minus sign of thesum of the vertical gradient values, and derives a vertical-relatedpixel difference value (S3208). Here, the sum of the vertical gradientvalues at the pair of relative pixel positions indicates the sum of thevertical gradient value at the relative pixel position in the firstrange and the vertical gradient value at the relative pixel position inthe second range. The vertical-related pixel difference value is thepixel difference value having the plus or minus sign inverted ormaintained according to the plus or minus sign of the sum of thevertical gradient values.

The circuitry of decoder 200 then derives, as a fourth parameter, thetotal sum of a plurality of horizontal-related pixel difference valuesderived respectively for the plurality of pairs of relative positions(S3209).

In addition, the circuitry of decoder 200 inverts or maintains the plusor minus sign of the sum of the horizontal gradient values derived forthe pair of relative pixel positions, according to the plus or minussign of the sum of the vertical gradient values, and derives avertical-related sum of horizontal gradient values (S3210). Here, thevertical-related sum of the horizontal gradient values indicates the sumof horizontal gradient values having the plus or minus sign inverted ormaintained according to the plus or minus sign of the sum of thevertical gradient values.

The circuitry of decoder 200 then derives, as a fifth parameter, thetotal sum of a plurality of vertical-related sums of horizontal gradientvalues derived respectively for the plurality of pairs of relative pixelpositions (S3211).

The circuitry of decoder 200 then generates a prediction image to beused to decode the current block using the first parameter, the secondparameter, the third parameter, the fourth parameter, and the fifthparameter (S3212).

In this way, substantial multiplication which requires a large amount ofcomputation in the computation performed for each pixel position may bereduced, which may make it possible to derive a plurality of parametersfor generating a prediction image with a low amount of computation.Accordingly, the processing amount in decoding may be reduced. Inaddition, the prediction image may be generated appropriately, based onthe plurality of parameters including the parameter related to thehorizontal gradient values, the parameter related to the verticalgradient values, and the parameter related to both the horizontalgradient values and the vertical gradient values.

In addition, for example, the circuitry of decoder 200 may derive asecond parameter according to Expression (11.1) described above, and asecond parameter according to Expression (11.2) described above. Inaddition, for example, the circuitry of decoder 200 may derive a thirdparameter according to Expression (11.3) described above, and a fourthparameter according to Expression (11.4) described above. In addition,for example, the circuitry of decoder 200 may derive a fifth parameteraccording to Expression (11.5) described above.

Here, Ω denotes a set of relative pixel positions, and [i, j] denoteseach of the relative pixel positions. For each of the plurality of pairsof relative pixel positions, I_(x) ⁰ denotes a horizontal gradient valueat a relative pixel position in the first range, and I_(x) ¹ denotes ahorizontal gradient value at a relative pixel position in the secondrange. For each of the plurality of pairs of relative pixel positions,I_(y) ⁰ denotes a vertical gradient value at a relative pixel positionin the first range, and I_(y) ¹ denotes a vertical gradient value at arelative pixel position in the second range.

For each of the plurality of pairs of relative pixel positions, I⁰denotes a pixel value at the relative pixel position in the first range,and I₁ denotes a pixel value at the relative pixel position in thesecond range. In addition, abs (I_(x) ¹+I_(x) ⁰) denotes an absolutevalue of I_(x) ¹+I_(x) ⁰, and sign (I_(x) ¹+I_(x) ⁰) denotes a plus orminus sign of I_(x) ¹+I_(x) ⁰. Also, abs (I_(y) ¹+I_(y) ⁰) denotes anabsolute value of I_(y) ¹+I_(y) ⁰, and sign (I_(y) ¹+I_(y) ⁰) denotes aplus or minus sign of I_(y) ¹+I_(y) ⁰.

In this way, a plurality of parameters may be derived with a low amountof computation using pixel values, horizontal gradient values, andvertical gradient values.

In addition, for example, the circuitry of decoder 200 may derive asixth parameter by dividing the third parameter by the first parameter.In addition, the circuitry of decoder 200 may derive a seventh parameterby subtracting a product of the fifth parameter and the sixth parameterfrom the fourth parameter, and dividing a result of the subtraction bythe second parameter. The circuitry of decoder 200 may then generate theprediction image using the sixth parameter and the seventh parameter.

In this way, a plurality of parameters may be appropriately integratedto two parameters corresponding to the horizontal direction and thevertical direction. The parameter related to the horizontal gradientvalues may be appropriately incorporated in the parameter correspondingto the horizontal direction. The parameter related to the verticalgradient values, the parameter related to both the horizontal gradientvalues and the vertical gradient values, and the parameter related tothe horizontal gradient values may be appropriately incorporated in theparameter corresponding to the vertical direction. A prediction imagemay be appropriately generated using the two parameters.

In addition, for example, the circuitry of decoder 200 may derive asixth parameter according to Expression (10.8) described above. Inaddition, for example, the circuitry of decoder 200 may derive a seventhparameter according to Expression (10.9) described above.

Here, sG_(x) denotes the first parameter, sG_(y) denotes the secondparameter, sG_(x)dI denotes the third parameter, sG_(y)dI denotes thefourth parameter, sG_(x)G_(y) denotes the fifth parameter, and u denotesthe sixth parameter. Bits is a function which returns a value obtainableby rounding up a binary logarithm of an argument to an integer.

In this way, two parameters corresponding to the horizontal directionand the vertical direction may be derived with a low amount ofcomputation.

In addition, the circuitry of decoder 200 may generate the predictionimage by deriving a prediction pixel value, using: a first pixel value;a first horizontal gradient value; a first vertical gradient value; asecond pixel value; a second horizontal gradient value; a secondvertical gradient value; the sixth parameter; and the seventh parameter.

Here, the prediction pixel value is the prediction pixel value at theposition of a current pixel included in the current block. The firstpixel value is the pixel value at a first pixel position correspondingto the position of the current pixel in the first reference block. Thefirst horizontal gradient value is a horizontal gradient value at thefirst pixel position. The second vertical gradient value is a verticalgradient value at the second pixel position. The second pixel value isthe pixel value at a second pixel position corresponding to the positionof the current pixel in the second reference block. The secondhorizontal gradient value is a horizontal gradient value at the secondpixel position. The second vertical gradient value is a verticalgradient value at the second pixel position.

This provides a possibility that the prediction image is generatedusing, for example, the two parameters corresponding to the horizontaldirection and the vertical direction, and the two parameterscorresponding to the horizontal direction and the vertical direction areappropriately reflected on the prediction image.

In addition, for example, the circuitry of decoder 200 may derive theprediction pixel value by dividing, by 2, a sum of the first pixelvalue, the second pixel value, a first correction value, and a secondcorrection value. Here, the first correction value corresponds to aproduct of a difference between the first horizontal gradient value andthe second horizontal gradient value and the sixth parameter, and thesecond correction value corresponds to a product of a difference betweenthe first vertical gradient value and the second vertical gradient valueand the seventh parameter.

In this way, a prediction image may be appropriately generated using,for example, the two parameters corresponding to the horizontaldirection and the vertical direction.

In addition, for example, the circuitry of decoder 200 may derive aprediction pixel value according to Expression (10.10) described above.Here, I⁰ denotes the first pixel value, I¹ denotes the second pixelvalue, u denotes the sixth parameter, I_(x) ⁰ denotes the firsthorizontal gradient value, I_(x) ¹ denotes the second horizontalgradient value, v denotes the seventh parameter, I_(y) ⁰ denotes thefirst vertical gradient value, and I_(y) ¹ denotes the second verticalgradient value. In this way, the prediction image may be appropriatelygenerated according to an expression related to, for example, the twoparameters corresponding to the horizontal direction and the verticaldirection.

In addition, for example, the circuitry of decoder 200 may derive atleast one parameter in a bi-directional optical flow using the firstparameter, the second parameter, the third parameter, the fourthparameter, and the fifth parameter, and generate the prediction imageusing the at least one parameter in the bi-directional optical flow andthe bi-directional optical flow. In this way, decoder 200 is capable ofappropriately generating the prediction image.

At least one parameter in the bi-directional optical flow may be one ofthe sixth parameter and the seventh parameter described above.

It is to be noted that inter predictor 218 of decoder 200 may performthe operation described above as the circuitry of decoder 200.

Other Examples

Encoder 100 and decoder 200 in each of the above-described examples maybe used as an image encoder and an image decoder, respectively, or maybe used as a video encoder and a video decoder, respectively.

Alternatively, each of encoder 100 and decoder 200 may be used as aprediction device. In other words, encoder 100 and decoder 200 maycorrespond to only inter predictor 126 and inter predictor 218,respectively. The other constituent elements may be included in otherdevices.

In addition, at least part of each of the examples described above maybe used as an encoding method or a decoding method, may be used as aprediction method, or may be used as another method.

In addition, each constituent element may be configured with dedicatedhardware, or may be implemented by executing a software program suitablefor the constituent element. Each constituent element may be implementedby a program executer such as a CPU or a processor reading and executinga software program recorded on a recording medium such as a hard disc ora semiconductor memory.

More specifically, each of encoder 100 and decoder 200 may includeprocessing circuitry and storage which is electrically connected to theprocessing circuitry and is accessible from the processing circuitry.For example, the processing circuitry corresponds to processor a1 or b1,and the storage corresponds to memory a2 or b2.

The processing circuitry includes at least one of the dedicated hardwareand the program executer, and executes processing using the storage. Inaddition, the storage stores a software program which is executed by theprogram executer when the processing circuitry includes the programexecuter.

Here, the software which implements either encoder 100, decoder 200, orthe like described above is a program indicated below.

For example, the program may cause a computer to execute an encodingmethod including: deriving an absolute value of a sum of horizontalgradient values which indicates an absolute value of a sum of ahorizontal gradient value at a relative pixel position in a first rangeand a horizontal gradient value at a relative pixel position in a secondrange, for each of a plurality of pairs of a relative pixel position inthe first range and a relative pixel position in the second range amonga plurality of pairs of relative pixel positions, the first rangeincluding a first reference block for a current block, the second rangeincluding a second reference block for the current block, the pluralityof pairs of relative pixel positions being determined commonly andrelatively for the first range and the second range; deriving, as afirst parameter, a total sum of a plurality of absolute values of sumsof horizontal gradient values derived respectively for the plurality ofpairs of relative pixel positions; deriving an absolute value of a sumof vertical gradient values which indicates an absolute value of a sumof a vertical gradient value at the relative pixel position in the firstrange and a vertical gradient value at the relative pixel position inthe second range, for each of the plurality of pairs of relative pixelpositions; deriving, as a second parameter, a total sum of a pluralityof absolute values of sums of vertical gradient values derivedrespectively for the plurality of pairs of relative pixel positions;deriving, for each of the plurality of pairs of relative pixelpositions, a pixel difference value which indicates a difference betweenthe pixel value at the relative pixel position in the first range andthe pixel value at the relative pixel position in the second range;inverting or maintaining a plus or minus sign of the pixel differencevalue derived for each of the plurality of pairs of relative pixelpositions, according to a plus or minus sign of the sum of thehorizontal gradient values which indicates the sum of the horizontalgradient value at the relative pixel position in the first range and thehorizontal gradient value at the relative pixel position in the secondrange, and deriving a horizontal-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the horizontal-related pixel difference value havingthe plus or minus sign inverted or maintained according to the plus orminus sign of the sum of the horizontal gradient values; deriving, as athird parameter, a total sum of a plurality horizontal-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverting or maintaining a plus or minus signof the pixel difference value derived for each of the plurality of pairsof relative pixel positions, according to a plus or minus sign of a sumof vertical gradient values which indicates a sum of the verticalgradient value at the relative pixel position in the first range and thevertical gradient value at the relative pixel position in the secondrange, and deriving a vertical-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the vertical-related pixel difference value having theplus or minus sign inverted or maintained according to the plus or minussign of the sum of the vertical gradient values; deriving, as a fourthparameter, a total sum of a plurality of vertical-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverting or maintaining a plus or minus signof the sum of the horizontal gradient values derived for each of theplurality of pairs of relative pixel positions, according to the plus orminus sign of the sum of the vertical gradient values, and deriving avertical-related sum of horizontal gradient values which indicates a sumof the horizontal gradient values having the plus or minus sign invertedor maintained according to the plus or minus sign of the sum of thevertical gradient values; deriving, as a fifth parameter, a total sum ofa plurality vertical-related sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions; andgenerating a prediction image to be used to encode the current blockusing the first parameter, the second parameter, the third parameter,the fourth parameter, and the fifth parameter.

For example, the program causes a computer to execute a decoding methodincluding: deriving an absolute value of a sum of horizontal gradientvalues which indicates an absolute value of a sum of a horizontalgradient value at a relative pixel position in a first range and ahorizontal gradient value at a relative pixel position in a secondrange, for each of a plurality of pairs of a relative pixel position inthe first range and a relative pixel position in the second range amonga plurality of pairs of relative pixel positions, the first rangeincluding a first reference block for a current block, the second rangeincluding a second reference block for the current block, the pluralityof pairs of relative pixel positions being determined commonly andrelatively for the first range and the second range; deriving, as afirst parameter, a total sum of a plurality of absolute values of sumsof horizontal gradient values derived respectively for the plurality ofpairs of relative pixel positions; deriving an absolute value of a sumof vertical gradient values which indicates an absolute value of a sumof a vertical gradient value at the relative pixel position in the firstrange and a vertical gradient value at the relative pixel position inthe second range, for each of the plurality of pairs of relative pixelpositions; deriving, as a second parameter, a total sum of a pluralityof absolute values of sums of vertical gradient values derivedrespectively for the plurality of pairs of relative pixel positions;deriving, for each of the plurality of pairs of relative pixelpositions, a pixel difference value which indicates a difference betweenthe pixel value at the relative pixel position in the first range andthe pixel value at the relative pixel position in the second range;inverting or maintaining a plus or minus sign of the pixel differencevalue derived for each of the plurality of pairs of relative pixelpositions, according to a plus or minus sign of the sum of thehorizontal gradient values which indicates the sum of the horizontalgradient value at the relative pixel position in the first range and thehorizontal gradient value at the relative pixel position in the secondrange, and deriving a horizontal-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the horizontal-related pixel difference value havingthe plus or minus sign inverted or maintained according to the plus orminus sign of the sum of the horizontal gradient values; deriving, as athird parameter, a total sum of a plurality horizontal-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverting or maintaining a plus or minus signof the pixel difference value derived for each of the plurality of pairsof relative pixel positions, according to a plus or minus sign of a sumof vertical gradient values which indicates a sum of the verticalgradient value at the relative pixel position in the first range and thevertical gradient value at the relative pixel position in the secondrange, and deriving a vertical-related pixel difference value whichindicates a pixel difference value derived for the pair of relativepixel positions, the vertical-related pixel difference value having theplus or minus sign inverted or maintained according to the plus or minussign of the sum of the vertical gradient values; deriving, as a fourthparameter, a total sum of a plurality of vertical-related pixeldifference values derived respectively for the plurality of pairs ofrelative pixel positions; inverting or maintaining a plus or minus signof the sum of the horizontal gradient values derived for each of theplurality of pairs of relative pixel positions, according to the plus orminus sign of the sum of the vertical gradient values, and deriving avertical-related sum of horizontal gradient values which indicates a sumof the horizontal gradient values having the plus or minus sign invertedor maintained according to the plus or minus sign of the sum of thevertical gradient values; deriving, as a fifth parameter, a total sum ofa plurality vertical-related sums of horizontal gradient values derivedrespectively for the plurality of pairs of relative pixel positions; andgenerating a prediction image to be used to decode the current blockusing the first parameter, the second parameter, the third parameter,the fourth parameter, and the fifth parameter.

In addition, each constituent element may be circuitry as describedabove. Circuits may compose circuitry as a whole, or may be separatecircuits. Alternatively, each constituent element may be implemented asa general processor, or may be implemented as an exclusive processor.

In addition, the process that is executed by a particular constituentelement may be executed by another constituent element. In addition, theprocessing execution order may be modified, or a plurality of processesmay be executed in parallel. In addition, an encoder and decoder mayinclude encoder 100 and decoder 200.

In addition, the ordinal numbers such as “first” and “second” used forexplanation may be changed appropriately. A new ordinal number may beattached to a constituent element, or the ordinal number attached to aconstituent element may be removed.

Although aspects of encoder 100 and decoder 200 have been describedbased on a plurality of examples, aspects of encoder 100 and decoder 200are not limited to these examples. The scope of the aspects of encoder100 and decoder 200 may encompass embodiments obtainable by adding, toany of these embodiments, various kinds of modifications that a personskilled in the art would arrive at without deviating from the scope ofthe present disclosure and embodiments configurable by combiningconstituent elements in different embodiments.

One or more of the aspects disclosed herein may be performed bycombining at least part of the other aspects in the present disclosure.In addition, one or more of the aspects disclosed herein may beperformed by combining, with other aspects, part of the processesindicated in any of the flow charts according to the aspects, part ofthe configuration of any of the devices, part of syntaxes, etc.

Implementations and Applications

As described in each of the above embodiments, each functional oroperational block may typically be realized as an MPU (micro processingunit) and memory, for example. Moreover, processes performed by each ofthe functional blocks may be realized as a program execution unit, suchas a processor which reads and executes software (a program) recorded ona recording medium such as ROM. The software may be distributed. Thesoftware may be recorded on a variety of recording media such assemiconductor memory. Note that each functional block can also berealized as hardware (dedicated circuit). Various combinations ofhardware and software may be employed.

The processing described in each of the embodiments may be realized viaintegrated processing using a single apparatus (system), and,alternatively, may be realized via decentralized processing using aplurality of apparatuses. Moreover, the processor that executes theabove-described program may be a single processor or a plurality ofprocessors. In other words, integrated processing may be performed, and,alternatively, decentralized processing may be performed.

Embodiments of the present disclosure are not limited to the aboveexemplary embodiments; various modifications may be made to theexemplary embodiments, the results of which are also included within thescope of the embodiments of the present disclosure.

Next, application examples of the moving picture encoding method (imageencoding method) and the moving picture decoding method (image decodingmethod) described in each of the above embodiments will be described, aswell as various systems that implement the application examples. Such asystem may be characterized as including an image encoder that employsthe image encoding method, an image decoder that employs the imagedecoding method, or an image encoder-decoder that includes both theimage encoder and the image decoder. Other configurations of such asystem may be modified on a case-by-case basis.

Usage Examples

FIG. 56 illustrates an overall configuration of content providing systemex100 suitable for implementing a content distribution service. The areain which the communication service is provided is divided into cells ofdesired sizes, and base stations ex106, ex107, ex108, ex109, and ex110,which are fixed wireless stations in the illustrated example, arelocated in respective cells.

In content providing system ex100, devices including computer ex111,gaming device ex112, camera ex113, home appliance ex114, and smartphoneex115 are connected to internet ex101 via internet service providerex102 or communications network ex104 and base stations ex106 throughex110. Content providing system ex100 may combine and connect anycombination of the above devices. In various implementations, thedevices may be directly or indirectly connected together via a telephonenetwork or near field communication, rather than via base stations ex106through ex110. Further, streaming server ex103 may be connected todevices including computer ex111, gaming device ex112, camera ex113,home appliance ex114, and smartphone ex115 via, for example, internetex101. Streaming server ex103 may also be connected to, for example, aterminal in a hotspot in airplane ex117 via satellite ex116.

Note that instead of base stations ex106 through ex110, wireless accesspoints or hotspots may be used. Streaming server ex103 may be connectedto communications network ex104 directly instead of via internet ex101or internet service provider ex102, and may be connected to airplaneex117 directly instead of via satellite ex116.

Camera ex113 is a device capable of capturing still images and video,such as a digital camera. Smartphone ex115 is a smartphone device,cellular phone, or personal handy-phone system (PHS) phone that canoperate under the mobile communications system standards of the 2G, 3G,3.9G, and 4G systems, as well as the next-generation 5G system.

Home appliance ex114 is, for example, a refrigerator or a deviceincluded in a home fuel cell cogeneration system.

In content providing system ex100, a terminal including an image and/orvideo capturing function is capable of, for example, live streaming byconnecting to streaming server ex103 via, for example, base stationex106. When live streaming, a terminal (e.g., computer ex111, gamingdevice ex112, camera ex113, home appliance ex114, smartphone ex115, or aterminal in airplane ex117) may perform the encoding processingdescribed in the above embodiments on still-image or video contentcaptured by a user via the terminal, may multiplex video data obtainedvia the encoding and audio data obtained by encoding audio correspondingto the video, and may transmit the obtained data to streaming serverex103. In other words, the terminal functions as the image encoderaccording to one aspect of the present disclosure.

Streaming server ex103 streams transmitted content data to clients thatrequest the stream. Client examples include computer ex111, gamingdevice ex112, camera ex113, home appliance ex114, smartphone ex115, andterminals inside airplane ex117, which are capable of decoding theabove-described encoded data. Devices that receive the streamed data maydecode and reproduce the received data. In other words, the devices mayeach function as the image decoder, according to one aspect of thepresent disclosure.

[Decentralized Processing]

Streaming server ex103 may be realized as a plurality of servers orcomputers between which tasks such as the processing, recording, andstreaming of data are divided. For example, streaming server ex103 maybe realized as a content delivery network (CDN) that streams content viaa network connecting multiple edge servers located throughout the world.In a CDN, an edge server physically near the client may be dynamicallyassigned to the client. Content is cached and streamed to the edgeserver to reduce load times. In the event of, for example, some type oferror or change in connectivity due, for example, to a spike in traffic,it is possible to stream data stably at high speeds, since it ispossible to avoid affected parts of the network by, for example,dividing the processing between a plurality of edge servers, orswitching the streaming duties to a different edge server and continuingstreaming.

Decentralization is not limited to just the division of processing forstreaming; the encoding of the captured data may be divided between andperformed by the terminals, on the server side, or both. In one example,in typical encoding, the processing is performed in two loops. The firstloop is for detecting how complicated the image is on a frame-by-frameor scene-by-scene basis, or detecting the encoding load. The second loopis for processing that maintains image quality and improves encodingefficiency. For example, it is possible to reduce the processing load ofthe terminals and improve the quality and encoding efficiency of thecontent by having the terminals perform the first loop of the encodingand having the server side that received the content perform the secondloop of the encoding. In such a case, upon receipt of a decodingrequest, it is possible for the encoded data resulting from the firstloop performed by one terminal to be received and reproduced on anotherterminal in approximately real time. This makes it possible to realizesmooth, real-time streaming.

In another example, camera ex113 or the like extracts a feature amount(an amount of features or characteristics) from an image, compressesdata related to the feature amount as metadata, and transmits thecompressed metadata to a server. For example, the server determines thesignificance of an object based on the feature amount and changes thequantization accuracy accordingly to perform compression suitable forthe meaning (or content significance) of the image. Feature amount datais particularly effective in improving the precision and efficiency ofmotion vector prediction during the second compression pass performed bythe server. Moreover, encoding that has a relatively low processingload, such as variable length coding (LC), may be handled by theterminal, and encoding that has a relatively high processing load, suchas context-adaptive binary arithmetic coding (CABAC), may be handled bythe server.

In yet another example, there are instances in which a plurality ofvideos of approximately the same scene are captured by a plurality ofterminals in, for example, a stadium, shopping mall, or factory. In sucha case, for example, the encoding may be decentralized by dividingprocessing tasks between the plurality of terminals that captured thevideos and, if necessary, other terminals that did not capture thevideos, and the server, on a per-unit basis. The units may be, forexample, groups of pictures (GOP), pictures, or tiles resulting fromdividing a picture. This makes it possible to reduce load times andachieve streaming that is closer to real time.

Since the videos are of approximately the same scene, management and/orinstructions may be carried out by the server so that the videoscaptured by the terminals can be cross-referenced. Moreover, the servermay receive encoded data from the terminals, change the referencerelationship between items of data, or correct or replace picturesthemselves, and then perform the encoding. This makes it possible togenerate a stream with increased quality and efficiency for theindividual items of data.

Furthermore, the server may stream video data after performingtranscoding to convert the encoding format of the video data. Forexample, the server may convert the encoding format from MPEG to VP(e.g., VP9), may convert H.264 to H.265, etc.

In this way, encoding can be performed by a terminal or one or moreservers. Accordingly, although the device that performs the encoding isreferred to as a “server” or “terminal” in the following description,some or all of the processes performed by the server may be performed bythe terminal, and likewise some or all of the processes performed by theterminal may be performed by the server. This also applies to decodingprocesses.

[3D, Multi-Angle]

There has been an increase in usage of images or videos combined fromimages or videos of different scenes concurrently captured, or of thesame scene captured from different angles, by a plurality of terminalssuch as camera ex113 and/or smartphone ex115. Videos captured by theterminals may be combined based on, for example, the separately obtainedrelative positional relationship between the terminals, or regions in avideo having matching feature points.

In addition to the encoding of two-dimensional moving pictures, theserver may encode a still image based on scene analysis of a movingpicture, either automatically or at a point in time specified by theuser, and transmit the encoded still image to a reception terminal.Furthermore, when the server can obtain the relative positionalrelationship between the video capturing terminals, in addition totwo-dimensional moving pictures, the server can generatethree-dimensional geometry of a scene based on video of the same scenecaptured from different angles. The server may separately encodethree-dimensional data generated from, for example, a point cloud and,based on a result of recognizing or tracking a person or object usingthree-dimensional data, may select or reconstruct and generate a videoto be transmitted to a reception terminal, from videos captured by aplurality of terminals.

This allows the user to enjoy a scene by freely selecting videoscorresponding to the video capturing terminals, and allows the user toenjoy the content obtained by extracting a video at a selected viewpointfrom three-dimensional data reconstructed from a plurality of images orvideos. Furthermore, as with video, sound may be recorded fromrelatively different angles, and the server may multiplex audio from aspecific angle or space with the corresponding video, and transmit themultiplexed video and audio.

In recent years, content that is a composite of the real world and avirtual world, such as virtual reality (VR) and augmented reality (AR)content, has also become popular. In the case of VR images, the servermay create images from the viewpoints of both the left and right eyes,and perform encoding that tolerates reference between the two viewpointimages, such as multi-view coding (MVC), and, alternatively, may encodethe images as separate streams without referencing. When the images aredecoded as separate streams, the streams may be synchronized whenreproduced, so as to recreate a virtual three-dimensional space inaccordance with the viewpoint of the user.

In the case of AR images, the server may superimpose virtual objectinformation existing in a virtual space onto camera informationrepresenting a real-world space, based on a three-dimensional positionor movement from the perspective of the user. The decoder may obtain orstore virtual object information and three-dimensional data, generatetwo-dimensional images based on movement from the perspective of theuser, and then generate superimposed data by seamlessly connecting theimages. Alternatively, the decoder may transmit, to the server, motionfrom the perspective of the user in addition to a request for virtualobject information. The server may generate superimposed data based onthree-dimensional data stored in the server in accordance with thereceived motion, and encode and stream the generated superimposed datato the decoder. Note that superimposed data typically includes, inaddition to RGB values, an a value indicating transparency, and theserver sets the a value for sections other than the object generatedfrom three-dimensional data to, for example, 0, and may perform theencoding while those sections are transparent. Alternatively, the servermay set the background to a determined RGB value, such as a chroma key,and generate data in which areas other than the object are set as thebackground. The determined RGB value may be predetermined.

Decoding of similarly streamed data may be performed by the client(e.g., the terminals), on the server side, or divided therebetween. Inone example, one terminal may transmit a reception request to a server,the requested content may be received and decoded by another terminal,and a decoded signal may be transmitted to a device having a display. Itis possible to reproduce high image quality data by decentralizingprocessing and appropriately selecting content regardless of theprocessing ability of the communications terminal itself. In yet anotherexample, while a TV, for example, is receiving image data that is largein size, a region of a picture, such as a tile obtained by dividing thepicture, may be decoded and displayed on a personal terminal orterminals of a viewer or viewers of the TV. This makes it possible forthe viewers to share a big-picture view as well as for each viewer tocheck his or her assigned area, or inspect a region in further detail upclose.

In situations in which a plurality of wireless connections are possibleover near, mid, and far distances, indoors or outdoors, it may bepossible to seamlessly receive content using a streaming system standardsuch as MPEG-DASH. The user may switch between data in real time whilefreely selecting a decoder or display apparatus including the user'sterminal, displays arranged indoors or outdoors, etc. Moreover, using,for example, information on the position of the user, decoding can beperformed while switching which terminal handles decoding and whichterminal handles the displaying of content. This makes it possible tomap and display information, while the user is on the move in route to adestination, on the wall of a nearby building in which a device capableof displaying content is embedded, or on part of the ground. Moreover,it is also possible to switch the bit rate of the received data based onthe accessibility to the encoded data on a network, such as when encodeddata is cached on a server quickly accessible from the receptionterminal, or when encoded data is copied to an edge server in a contentdelivery service.

[Scalable Encoding]

The switching of content will be described with reference to a scalablestream, illustrated in FIG. 57, which is compression coded viaimplementation of the moving picture encoding method described in theabove embodiments. The server may have a configuration in which contentis switched while making use of the temporal and/or spatial scalabilityof a stream, which is achieved by division into and encoding of layers,as illustrated in FIG. 57. Note that there may be a plurality ofindividual streams that are of the same content but different quality.In other words, by determining which layer to decode based on internalfactors, such as the processing ability on the decoder side, andexternal factors, such as communication bandwidth, the decoder side canfreely switch between low resolution content and high resolution contentwhile decoding. For example, in a case in which the user wants tocontinue watching, for example at home on a device such as a TVconnected to the internet, a video that the user had been previouslywatching on smartphone ex115 while on the move, the device can simplydecode the same stream up to a different layer, which reduces the serverside load.

Furthermore, in addition to the configuration described above, in whichscalability is achieved as a result of the pictures being encoded perlayer, with the enhancement layer being above the base layer, theenhancement layer may include metadata based on, for example,statistical information on the image. The decoder side may generate highimage quality content by performing super-resolution imaging on apicture in the base layer based on the metadata. Super-resolutionimaging may improve the SN ratio while maintaining resolution and/orincreasing resolution. Metadata includes information for identifying alinear or a non-linear filter coefficient, as used in super-resolutionprocessing, or information identifying a parameter value in filterprocessing, machine learning, or a least squares method used insuper-resolution processing.

Alternatively, a configuration may be provided in which a picture isdivided into, for example, tiles in accordance with, for example, themeaning of an object in the image. On the decoder side, only a partialregion is decoded by selecting a tile to decode. Further, by storing anattribute of the object (person, car, ball, etc.) and a position of theobject in the video (coordinates in identical images) as metadata, thedecoder side can identify the position of a desired object based on themetadata and determine which tile or tiles include that object. Forexample, as illustrated in FIG. 58, metadata may be stored using a datastorage structure different from pixel data, such as an SEI(supplemental enhancement information) message in HEVC. This metadataindicates, for example, the position, size, or color of the main object.

Metadata may be stored in units of a plurality of pictures, such asstream, sequence, or random access units. The decoder side can obtain,for example, the time at which a specific person appears in the video,and by fitting the time information with picture unit information, canidentify a picture in which the object is present, and can determine theposition of the object in the picture.

[Web Page Optimization]

FIG. 59 illustrates an example of a display screen of a web page oncomputer ex111, for example. FIG. 60 illustrates an example of a displayscreen of a web page on smartphone ex115, for example. As illustrated inFIG. 59 and FIG. 60, a web page may include a plurality of image linksthat are links to image content, and the appearance of the web page maydiffer depending on the device used to view the web page. When aplurality of image links are viewable on the screen, until the userexplicitly selects an image link, or until the image link is in theapproximate center of the screen or the entire image link fits in thescreen, the display apparatus (decoder) may display, as the image links,still images included in the content or I pictures; may display videosuch as an animated gif using a plurality of still images or I pictures;or may receive only the base layer, and decode and display the video.

When an image link is selected by the user, the display apparatusperforms decoding while, for example, giving the highest priority to thebase layer. Note that if there is information in the HTML code of theweb page indicating that the content is scalable, the display apparatusmay decode up to the enhancement layer. Further, in order to guaranteereal-time reproduction, before a selection is made or when the bandwidthis severely limited, the display apparatus can reduce delay between thepoint in time at which the leading picture is decoded and the point intime at which the decoded picture is displayed (that is, the delaybetween the start of the decoding of the content to the displaying ofthe content) by decoding and displaying only forward reference pictures(I picture, P picture, forward reference B picture). Still further, thedisplay apparatus may purposely ignore the reference relationshipbetween pictures, and coarsely decode all B and P pictures as forwardreference pictures, and then perform normal decoding as the number ofpictures received over time increases.

[Autonomous Driving]

When transmitting and receiving still image or video data such as two-or three-dimensional map information for autonomous driving or assisteddriving of an automobile, the reception terminal may receive, inaddition to image data belonging to one or more layers, information on,for example, the weather or road construction as metadata, and associatethe metadata with the image data upon decoding. Note that metadata maybe assigned per layer and, alternatively, may simply be multiplexed withthe image data.

In such a case, since the automobile, drone, airplane, etc., containingthe reception terminal is mobile, the reception terminal may seamlesslyreceive and perform decoding while switching between base stations amongbase stations ex106 through ex110 by transmitting information indicatingthe position of the reception terminal. Moreover, in accordance with theselection made by the user, the situation of the user, and/or thebandwidth of the connection, the reception terminal may dynamicallyselect to what extent the metadata is received, or to what extent themap information, for example, is updated.

In content providing system ex100, the client may receive, decode, andreproduce, in real time, encoded information transmitted by the user.

[Streaming of Individual Content]

In content providing system ex100, in addition to high image quality,long content distributed by a video distribution entity, unicast ormulticast streaming of low image quality, and short content from anindividual are also possible. Such content from individuals is likely tofurther increase in popularity. The server may first perform editingprocessing on the content before the encoding processing, in order torefine the individual content. This may be achieved using the followingconfiguration, for example.

In real time while capturing video or image content, or after thecontent has been captured and accumulated, the server performsrecognition processing based on the raw data or encoded data, such ascapture error processing, scene search processing, meaning analysis,and/or object detection processing. Then, based on the result of therecognition processing, the server—either when prompted orautomatically—edits the content, examples of which include: correctionsuch as focus and/or motion blur correction; removing low-priorityscenes such as scenes that are low in brightness compared to otherpictures, or out of focus; object edge adjustment; and color toneadjustment. The server encodes the edited data based on the result ofthe editing. It is known that excessively long videos tend to receivefewer views. Accordingly, in order to keep the content within a specificlength that scales with the length of the original video, the servermay, in addition to the low-priority scenes described above,automatically clip out scenes with low movement, based on an imageprocessing result. Alternatively, the server may generate and encode avideo digest based on a result of an analysis of the meaning of a scene.

There may be instances in which individual content may include contentthat infringes a copyright, moral right, portrait rights, etc. Suchinstance may lead to an unfavorable situation for the creator, such aswhen content is shared beyond the scope intended by the creator.Accordingly, before encoding, the server may, for example, edit imagesso as to blur faces of people in the periphery of the screen or blur theinside of a house, for example. Further, the server may be configured torecognize the faces of people other than a registered person in imagesto be encoded, and when such faces appear in an image, may apply amosaic filter, for example, to the face of the person. Alternatively, aspre- or post-processing for encoding, the user may specify, forcopyright reasons, a region of an image including a person or a regionof the background to be processed. The server may process the specifiedregion by, for example, replacing the region with a different image, orblurring the region. If the region includes a person, the person may betracked in the moving picture, and the person's head region may bereplaced with another image as the person moves.

Since there is a demand for real-time viewing of content produced byindividuals, which tends to be small in data size, the decoder may firstreceive the base layer as the highest priority, and perform decoding andreproduction, although this may differ depending on bandwidth. When thecontent is reproduced two or more times, such as when the decoderreceives the enhancement layer during decoding and reproduction of thebase layer, and loops the reproduction, the decoder may reproduce a highimage quality video including the enhancement layer. If the stream isencoded using such scalable encoding, the video may be low quality whenin an unselected state or at the start of the video, but it can offer anexperience in which the image quality of the stream progressivelyincreases in an intelligent manner. This is not limited to just scalableencoding; the same experience can be offered by configuring a singlestream from a low quality stream reproduced for the first time and asecond stream encoded using the first stream as a reference.

Other Implementation and Application Examples

The encoding and decoding may be performed by LSI (large scaleintegration circuitry) ex500 (see FIG. 56), which is typically includedin each terminal. LSI ex500 may be configured of a single chip or aplurality of chips. Software for encoding and decoding moving picturesmay be integrated into some type of a recording medium (such as aCD-ROM, a flexible disk, or a hard disk) that is readable by, forexample, computer ex111, and the encoding and decoding may be performedusing the software. Furthermore, when smartphone ex115 is equipped witha camera, the video data obtained by the camera may be transmitted. Inthis case, the video data may be coded by LSI ex500 included insmartphone ex115.

Note that LSI ex500 may be configured to download and activate anapplication. In such a case, the terminal first determines whether it iscompatible with the scheme used to encode the content, or whether it iscapable of executing a specific service. When the terminal is notcompatible with the encoding scheme of the content, or when the terminalis not capable of executing a specific service, the terminal may firstdownload a codec or application software and then obtain and reproducethe content.

Aside from the example of content providing system ex100 that usesinternet ex101, at least the moving picture encoder (image encoder) orthe moving picture decoder (image decoder) described in the aboveembodiments may be implemented in a digital broadcasting system. Thesame encoding processing and decoding processing may be applied totransmit and receive broadcast radio waves superimposed with multiplexedaudio and video data using, for example, a satellite, even though thisis geared toward multicast, whereas unicast is easier with contentproviding system ex100.

[Hardware Configuration]

FIG. 61 illustrates further details of smartphone ex115 shown in FIG.56. FIG. 62 illustrates a configuration example of smartphone ex115.Smartphone ex115 includes antenna ex450 for transmitting and receivingradio waves to and from base station ex110, camera ex465 capable ofcapturing video and still images, and display ex458 that displaysdecoded data, such as video captured by camera ex465 and video receivedby antenna ex450. Smartphone ex115 further includes user interface ex466such as a touch panel, audio output unit ex457 such as a speaker foroutputting speech or other audio, audio input unit ex456 such as amicrophone for audio input, memory ex467 capable of storing decoded datasuch as captured video or still images, recorded audio, received videoor still images, and mail, as well as decoded data, and slot ex464 whichis an interface for SIM ex468 for authorizing access to a network andvarious data. Note that external memory may be used instead of memoryex467.

Main controller ex460, which may comprehensively control display ex458and user interface ex466, power supply circuit ex461, user interfaceinput controller ex462, video signal processor ex455, camera interfaceex463, display controller ex459, modulator/demodulator ex452,multiplexer/demultiplexer ex453, audio signal processor ex454, slotex464, and memory ex467 are connected via bus ex470.

When the user turns on the power button of power supply circuit ex461,smartphone ex115 is powered on into an operable state, and eachcomponent is supplied with power from a battery pack.

Smartphone ex115 performs processing for, for example, calling and datatransmission, based on control performed by main controller ex460, whichincludes a CPU, ROM, and RAM. When making calls, an audio signalrecorded by audio input unit ex456 is converted into a digital audiosignal by audio signal processor ex454, to which spread spectrumprocessing is applied by modulator/demodulator ex452 and digital-analogconversion, and frequency conversion processing is applied bytransmitter/receiver ex451, and the resulting signal is transmitted viaantenna ex450. The received data is amplified, frequency converted, andanalog-digital converted, inverse spread spectrum processed bymodulator/demodulator ex452, converted into an analog audio signal byaudio signal processor ex454, and then output from audio output unitex457. In data transmission mode, text, still-image, or video data maybe transmitted under control of main controller ex460 via user interfaceinput controller ex462 based on operation of user interface ex466 of themain body, for example. Similar transmission and reception processing isperformed. In data transmission mode, when sending a video, still image,or video and audio, video signal processor ex455 compression encodes,via the moving picture encoding method described in the aboveembodiments, a video signal stored in memory ex467 or a video signalinput from camera ex465, and transmits the encoded video data tomultiplexer/demultiplexer ex453. Audio signal processor ex454 encodes anaudio signal recorded by audio input unit ex456 while camera ex465 iscapturing a video or still image, and transmits the encoded audio datato multiplexer/demultiplexer ex453. Multiplexer/demultiplexer ex453multiplexes the encoded video data and encoded audio data using adetermined scheme, modulates and converts the data usingmodulator/demodulator (modulator/demodulator circuit) ex452 andtransmitter/receiver ex451, and transmits the result via antenna ex450.The determined scheme may be predetermined.

When video appended in an email or a chat, or a video linked from a webpage, is received, for example, in order to decode the multiplexed datareceived via antenna ex450, multiplexer/demultiplexer ex453demultiplexes the multiplexed data to divide the multiplexed data into abitstream of video data and a bitstream of audio data, supplies theencoded video data to video signal processor ex455 via synchronous busex470, and supplies the encoded audio data to audio signal processorex454 via synchronous bus ex470. Video signal processor ex455 decodesthe video signal using a moving picture decoding method corresponding tothe moving picture encoding method described in the above embodiments,and video or a still image included in the linked moving picture file isdisplayed on display ex458 via display controller ex459. Audio signalprocessor ex454 decodes the audio signal and outputs audio from audiooutput unit ex457. Since real-time streaming is becoming increasinglypopular, there may be instances in which reproduction of the audio maybe socially inappropriate, depending on the user's environment.Accordingly, as an initial value, a configuration in which only videodata is reproduced, i.e., the audio signal is not reproduced, may bepreferable; audio may be synchronized and reproduced only when an input,such as when the user clicks video data, is received.

Although smartphone ex115 was used in the above example, otherimplementations are conceivable: a transceiver terminal including bothan encoder and a decoder; a transmitter terminal including only anencoder; and a receiver terminal including only a decoder. In thedescription of the digital broadcasting system, an example is given inwhich multiplexed data obtained as a result of video data beingmultiplexed with audio data is received or transmitted. The multiplexeddata, however, may be video data multiplexed with data other than audiodata, such as text data related to the video. Further, the video dataitself rather than multiplexed data may be received or transmitted.

Although main controller ex460 including a CPU is described ascontrolling the encoding or decoding processes, various terminals ofteninclude GPUs. Accordingly, a configuration is acceptable in which alarge area is processed at once by making use of the performance abilityof the GPU via memory shared by the CPU and GPU, or memory including anaddress that is managed so as to allow common usage by the CPU and GPU.This makes it possible to shorten encoding time, maintain the real-timenature of the stream, and reduce delay. In particular, processingrelating to motion estimation, deblocking filtering, sample adaptiveoffset (SAO), and transformation/quantization can be effectively carriedout by the GPU instead of the CPU in units of pictures, for example, allat once.

Although only some exemplary embodiments of the present disclosure havebeen described in detail above, those skilled in the art will readilyappreciate that many modifications are possible in the exemplaryembodiments without materially departing from the novel teachings andadvantages of the present disclosure. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure.

INDUSTRIAL APPLICABILITY

The present disclosure is applicable to, for example, televisionreceivers, digital video recorders, car navigation systems, mobilephones, digital cameras, digital video cameras, teleconferencingsystems, electronic mirrors, etc.

1-9. (canceled)
 10. A decoder comprising: a memory; and a processorconnected to the memory and configured to generate a prediction image inorder to decode a current block based on a first parameter, a secondparameter, a third parameter, a fourth parameter, and a fifth parameterthat are derived in a bi-directional optical flow (BDOF) process,wherein the first parameter is derived based on the followingexpression:Σ_([i,j]∈Ω)abs(I _(x) ¹ +I _(x) ⁰);  [Math. 1] the second parameter isderived based on the following expression:Σ_([i,j]∈Ω)abs(I _(y) ¹ +I _(y) ⁰);  [Math. 2] the third parameter isderived based on the following expression:Σ_([i,j]∈Ω)(−sign(I _(x) ¹ +I _(x) ⁰)×(I ⁰ −I ¹));  [Math. 3] the fourthparameter is derived based on the following expression:Σ_([i,j]∈Ω)(−sign(I _(y) ¹ +I _(y) ⁰)×(I ⁰ −I ¹)); and  [Math. 4] thefifth parameter is derived based on the following expression,[Math. 5](sign(I _(y) ¹ +I _(y) ⁰)×(I _(x) ¹ +I _(x) ⁰)),  [Math. 5]where: Ω indicates a set of relative pixel positions; [i, j] indicates arelative pixel position in the set Ω defined by a horizontal position iand a vertical position j; I_(x) ⁰ indicates a horizontal gradient valueat a first pixel position in a first gradient image, and I_(x) ¹indicates a horizontal gradient value at the first pixel position in asecond gradient image, the first pixel position being determined basedon a relative pixel position [i, j], the first gradient image and thesecond gradient image corresponding to the current block; I_(y) ⁰indicates a vertical gradient value at the first pixel position in thefirst gradient image, and I_(y) ¹ indicates a vertical gradient value atthe first pixel position in the second gradient image; I⁰ indicates apixel value at the first pixel position in a first interpolated imagecorresponding to the current block; I¹ indicates a pixel value at thefirst pixel position in a second interpolated image corresponding to thecurrent block; the abs function outputs an absolute value of anargument; and the sign function outputs a sign of an argument which is−1, 0, or
 1. 11. A non-transitory computer readable medium storing abitstream, the bitstream comprising a prediction parameter whichindicates a prediction process among prediction process candidates andwhich is read by a decoder to decode a current block provided in thebitstream, the prediction process candidates including a bi-directionaloptical flow (BDOF) process in which a first parameter, a secondparameter, a third parameter, a fourth parameter, and a fifth parameterare used to generate a prediction image of the current block, whereinthe first parameter is derived based on the following expression:Σ_([i,j]∈Ω)abs(I _(x) ¹ +I _(x) ⁰);  [Math. 1] the second parameter isderived based on the following expression:Σ_([i,j]∈Ω)abs(I _(y) ¹ +I _(y) ⁰);  [Math. 2] the third parameter isderived based on the following expression:Σ_([i,j]∈Ω)(−sign(I _(x) ¹ +I _(x) ⁰)×(I ⁰ −I ¹));  [Math. 3] the fourthparameter is derived based on the following expression:Σ_([i,j]∈Ω)(−sign(I _(y) ¹ +I _(y) ⁰)×(I ⁰ −I ¹)); and  [Math. 4] thefifth parameter is derived based on the following expression,Σ_([i,j]∈Ω)(sign(I _(y) ¹ +I _(y) ⁰)×N(I _(x) ¹ +I _(x) ⁰)),  [Math. 5]where: Ω indicates a set of relative pixel positions; [i, j] indicates arelative pixel position in the set Ω defined by a horizontal position iand a vertical position j; I_(x) ⁰ indicates a horizontal gradient valueat a first pixel position in a first gradient image, and I_(x) ¹indicates a horizontal gradient value at the first pixel position in asecond gradient image, the first pixel position being determined basedon a relative pixel position [i, j], the first gradient image and thesecond gradient image corresponding to the current block; I_(y) ⁰indicates a vertical gradient value at the first pixel position in thefirst gradient image, and I_(y) ¹ indicates a vertical gradient value atthe first pixel position in the second gradient image; I⁰ indicates apixel value at the first pixel position in a first interpolated imagecorresponding to the current block; I¹ indicates a pixel value at thefirst pixel position in a second interpolated image corresponding to thecurrent block; the abs function outputs an absolute value of anargument; and the sign function outputs a sign of an argument which is−1, 0, or 1.